## Journal of Applied Analysis and Computation

 Short Title: J. Appl. Anal. Comput. Publisher: Wilmington Scientific Publisher, Wilmington, NC; Shanghai Normal University, Shanghai ISSN: 2156-907X; 2158-5644/e Online: http://jaac.ijournal.cn/ch/reader/issue_browser.aspx Comments: Indexed cover-to-cover; This journal is available open access
 Documents Indexed: 792 Publications (since 2011) References Indexed: 592 Publications with 17,739 References.
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### Latest Issues

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### Authors

 9 Guo, Boling 9 Han, Maoan 8 Li, Jibin 8 Yang, Bicheng 7 Jiang, Weihua 6 Cong, Yuhao 6 Meng, Fanwei 6 Xu, Rui 5 Bai, Yuzhen 5 Chen, Fangqi 5 Cheng, Zhibo 5 Li, Xianyi 5 Li, Yong 5 Miranville, Alain M. 5 Xia, Yonghui 5 Zhang, Lijun 5 Zhou, Zhengxin 4 Al-saedi, Ahmed Eid Salem 4 Du, Xianyun 4 Elsayed, Elsayed Mohammed 4 Giné, Jaume 4 Graef, John R. 4 Gu, Beiqing 4 Huang, Wentao 4 Javidi, Mohammad 4 Li, Dongping 4 Li, Yongjun 4 Llibre, Jaume 4 O’Regan, Donal 4 Sadigh Behzadi, Shadan 4 Shi, Bao 4 Tang, Shengqiang 4 Wang, Ronghua 4 Yan, Litan 4 You, Yuncheng 4 Zhang, Linghai 3 Afrouzi, Ghasem Alizadeh 3 Agarwal, Ravi P. 3 Ahmad, Bashir 3 An, Yukun 3 Balachandran, Krishnan 3 Chen, Guanrong 3 Chen, Huiqin 3 Dash, Gouranga Charan 3 Elsaid, Ahmed 3 Fan, Meng 3 Gou, Haide 3 Han, Zhenlai 3 Hong, Xiaochun 3 Huang, Ting-Zhu 3 Huo, Hai-Feng 3 Jiang, Daqing 3 Jiang, Heping 3 Jiang, Xiaoyu 3 Jin, Zhen 3 Kang, Shugui 3 Khalique, Chaudry Masood 3 Lan, Kunquan 3 Li, Fushan 3 Li, Jianquan 3 Li, Jicheng 3 Li, Meili 3 Li, Na 3 Li, Yangrong 3 Li, Yongxiang 3 Liu, Haidong 3 Liu, Hanze 3 Liu, Yirong 3 Liu, Zhisu 3 Lou, Jie 3 Lu, Junliang 3 Ma, Changfeng 3 Ma, Shiwang 3 Meng, Xinzhu 3 Ni, Mingkang 3 Ouaro, Stanislas 3 Park, Choonkil 3 Qi, Feng 3 Qin, Xiaolong 3 Quintanilla de Latorre, Ramón 3 Ren, Jingli 3 Shao, Jing 3 Shao, Zhiqiang 3 Song, Jie 3 Tang, Chunlei 3 Tian, Lixin 3 Tripathy, Arun Kumar 3 Tunç, Cemil 3 Wang, Haijun 3 Wang, Qinlong 3 Wei, Jinying 3 Xie, Shengli 3 Xu, Jiafa 3 Xu, Xiaoling 3 Yan, Zuomao 3 Yang, Junmin 3 Yu, Pei 3 Yu, Yongguang 3 Yuan, Sanling 3 Zhai, Chengbo ...and 1,340 more Authors
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### Fields

 319 Ordinary differential equations (34-XX) 269 Partial differential equations (35-XX) 141 Biology and other natural sciences (92-XX) 113 Dynamical systems and ergodic theory (37-XX) 95 Numerical analysis (65-XX) 70 Operator theory (47-XX) 48 Real functions (26-XX) 40 Systems theory; control (93-XX) 39 Difference and functional equations (39-XX) 38 Probability theory and stochastic processes (60-XX) 37 Fluid mechanics (76-XX) 21 Integral equations (45-XX) 20 Operations research, mathematical programming (90-XX) 18 Calculus of variations and optimal control; optimization (49-XX) 18 Mechanics of deformable solids (74-XX) 17 Linear and multilinear algebra; matrix theory (15-XX) 16 Functions of a complex variable (30-XX) 12 Special functions (33-XX) 12 Computer science (68-XX) 11 Global analysis, analysis on manifolds (58-XX) 11 Classical thermodynamics, heat transfer (80-XX) 11 Information and communication theory, circuits (94-XX) 10 Statistics (62-XX) 9 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 7 Combinatorics (05-XX) 7 General topology (54-XX) 5 Abstract harmonic analysis (43-XX) 5 Functional analysis (46-XX) 5 Mechanics of particles and systems (70-XX) 5 Optics, electromagnetic theory (78-XX) 4 Number theory (11-XX) 4 Nonassociative rings and algebras (17-XX) 4 Integral transforms, operational calculus (44-XX) 3 Sequences, series, summability (40-XX) 3 Geophysics (86-XX) 2 Measure and integration (28-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Approximations and expansions (41-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Algebraic geometry (14-XX) 1 Associative rings and algebras (16-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Geometry (51-XX) 1 Quantum theory (81-XX) 1 Statistical mechanics, structure of matter (82-XX)

### Citations contained in zbMATH Open

416 Publications have been cited 1,330 times in 1,175 Documents Cited by Year
Cross-diffusion induced instability and stability in reaction-diffusion systems. Zbl 1304.35329
Shi, Junping; Xie, Zhifu; Little, Kristina
2011
Existence of generalized traveling waves in time recurrent and space periodic monostable equations. Zbl 1304.35351
Shen, Wenxian
2011
Bifurcation of limit cycles in piecewise smooth systems via Melnikov function. Zbl 1451.37073
Han, Maoan; Sheng, Lijuan
2015
On the maximum number of periodic solutions of piecewise smooth periodic equations by average method. Zbl 1474.37050
Han, Maoan
2017
Asymptotic behavior of the Cahn-Hilliard-Oono equation. Zbl 1304.35342
Miranville, Alain
2011
Global dynamics analysis of a nonlinear impulsive stochastic chemostat system in a polluted environment. Zbl 1463.34196
Meng, Xinzhu; Wang, Lu; Zhang, Tonghua
2016
Bifurcation of limit cycles in small perturbations of a hyper-elliptic Hamiltonian system with two nilpotent saddles. Zbl 1319.34067
Kazemi, Rasool; Zangeneh, Hamid R. Z.
2012
Existence theorems and Hyers-Ulam stability for a class of hybrid fractional differential equations with $$p$$-Laplacian operator. Zbl 1461.34009
Khan, Hasib; Tunc, Cemil; Chen, Wen; Khan, Aziz
2018
Some quantum estimates of Hermite-Hadamard inequalities for convex functions. Zbl 1488.26117
Liu, Wenjun; Zhuang, Hefeng
2017
Bifurcation of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems of degree 5 with a cusp. Zbl 1304.34058
Atabaigi, Ali; Zangeneh, Hamid R. Z.
2011
A cubic differential system with nine limit cycles. Zbl 1304.34062
Lloyd, Noel G.; Pearson, Jane Margaret
2012
Chaotic behavior in a new fractional-order love triangle system with competition. Zbl 1330.91162
Liu, Wenjun; Chen, Kewang
2015
Strong convergence analysis of a hybrid algorithm for nonlinear operators in a Banach space. Zbl 07303041
Cho, Sun Young
2018
On the limit cycles of a kind of Liénard system with a nilpotent center under perturbations. Zbl 1304.34063
Yang, Junmin
2012
Analysis of dynamics in a complex food chain with ratio-dependent functional response. Zbl 1292.34044
Freeze, Michael; Chang, Yaw; Feng, Wei
2014
Turing-Hopf bifurcation in the reaction-diffusion system with delay and application to a diffusive predator-prey model. Zbl 1461.35035
Song, Yongli; Jiang, Heping; Yuan, Yuan
2019
A search for lump solutions to a combined fourth-order nonlinear PDE in (2+1)-dimensions. Zbl 1464.35287
Ma, Wen-Xiu
2019
Entropy solutions to nonlinear elliptic anisotropic problem with variable exponent. Zbl 1316.35104
Benboubker, Mohamed Badr; Hjiaj, Hassane; Ouaro, Stanislas
2014
Fixed point theorems for generalized weakly $$S$$-contractive mappings in partial metric spaces. Zbl 1441.54035
Mishra, Lakshmi Narayan; Tiwari, Shiv Kant; Mishra, Vishnu Narayan
2015
Analysis of the binge drinking models with demographics and nonlinear infectivity on networks. Zbl 1457.92183
Xiang, Hong; Wang, Yanyan; Huo, Haifeng
2018
Homoclinic solutions of discrete nonlinear systems via variational method. Zbl 1462.39003
Erbe, Lynn; Jia, Baoguo; Zhang, Qinqin
2019
Long time behavior of an Allen-Cahn type equation with a singular potential and dynamic boundary conditions. Zbl 1304.35612
Israel, Haydi
2012
Spectrum comparison for a conserved reaction-diffusion system with a variational property. Zbl 1304.35336
Morita, Yoshihisa
2012
A study on Zoladek’s example. Zbl 1304.34064
Yu, Pei; Han, Maoan
2011
Explicit soliton solutions of the Kaup-Kupershmidt equation through the dynamical system approach. Zbl 1304.35616
Li, Jibin; Qiao, Zhijun
2011
Solving nonlinear ordinary differential equations using the NDM. Zbl 1330.35433
Rawashdeh, Mahmoud Saleh; Maitama, Shehu
2015
Several formulas for special values of the Bell polynomials of the second kind and applications. Zbl 1474.05006
Qi, Feng; Shi, Xiaoting; Liu, Fangfang; Kruchinin, Dmitry V.
2017
Stability results and existence theorems for nonlinear delay-fractional differential equations with $$\varphi_p^*$$-operator. Zbl 1464.34103
Khan, Hasib; Tunc, Cemil; Khan, Aziz
2020
Integrability conditions for complex systems with homogeneous quintic nonlinearities. Zbl 1304.34055
Ferčec, Brigita; Chen, Xingwu; Romanovski, Valery G.
2011
Dynamics of stage-structured discrete mosquito population models. Zbl 1304.39009
Lu, Junliang; Li, Jia
2011
On a new model of two-patch predator-prey system with migration of both species. Zbl 1304.92110
Feng, Wei; Rock, Brevin; Hinson, Jody
2011
Oscillation criteria for a class of first order neutral impulsive differential-difference equations. Zbl 1292.34066
Tripathy, Arun Kumar
2014
Analytical solution of time-fractional two-component evolutionary system of order 2 by residual power series method. Zbl 1447.35111
Alquran, Marwan
2015
A logarithmically completely monotonic function involving the ratio of gamma functions. Zbl 1447.33002
Qi, Feng; Li, Wen-Hui
2015
General energy decay for a degenerate viscoelastic Petrovsky-type plate equation with boundary feedback. Zbl 1456.35035
Li, Fushan; Du, Guangwei
2018
A new iterative method for solving split feasibility problem. Zbl 07331945
Garodia, Chanchal; Uddin, Izhar
2020
Spatiotemporal dynamics of a predator-prey model incorporating a prey refuge. Zbl 1300.92089
Sambath, M.; Balachandran, K.
2013
Notes on exact travelling wave solutions for a long wave-short wave model. Zbl 1378.34003
Li, Jibin
2015
Analysis of the time fractional nonlinear diffusion equation from diffusion process. Zbl 1480.35394
Liu, Jian-Gen; Yang, Xiao-Jun; Feng, Yi-Ying; Zhang, Hong-Yi
2020
Effect of herd shape in a diffusive predator-prey model with time delay. Zbl 1465.92147
Djilali, Salih
2019
A numerical solution of nonlinear Volterra-Fredholm integral equations. Zbl 1293.65175
Zarebnia, M.
2013
Cyclicity of several quadratic reversible systems with center of genus one. Zbl 1304.34059
Chen, Long; Ma, Xianzhong; Zhang, Gemeng; Li, Chengzhi
2011
Application of homotopy analysis method for solving a class of nonlinear Volterra-Fredholm integro-differential equations. Zbl 1304.34110
2012
Stability and traveling waves of diffusive predator-prey model with age-structure and nonlocal effect. Zbl 1304.92112
Hong, Kai; Weng, Peixuan
2012
Global stability of a virus infection model with two delays and two types of target cells. Zbl 1304.92122
Li, Jianquan; Song, Xiuchao; Gao, Fengyin
2012
Soliton solutions of shallow water wave equations by means of $$G'/G$$ expansion method. Zbl 1310.74028
Alquran, Marwan; Qawasmeh, Aminah
2014
Smooth solution of partial integro-differential equations using radial basis functions. Zbl 1297.35260
Avazzadeh, Z.; Heydari, M.; Chen, W.; Loghmani, G. B.
2014
Entropy solutions for nonlinear nonhomogeneous Neumann problems involving the generalized $$p(x)$$-Laplace operator. Zbl 1303.35008
Azroul, E.; Benboubker, M. B.; Ouaro, S.
2013
Numerical analysis for a locally damped wave equation. Zbl 1288.65144
Rincon, M. A.; Copetti, M. I. M.
2013
Existence-uniqueness problems for infinited dimensional stochastic differential equations with delays. Zbl 1319.34141
Xu, Daoyi; Wang, Xiaohu; Yang, Zhiguo
2012
Double Hopf bifurcation and chaos in Liu system with delayed feedback. Zbl 1304.34123
Ding, Yuting; Jiang, Weihua
2011
Spatial spread of rabies in China. Zbl 1304.92126
Zhang, Juan; Jin, Zhen; Sun, Guiquan; Sun, Xiangdong; Ruan, Shigui
2012
Stability and Neimark-Sacker bifurcation of a semi-discrete population model. Zbl 1323.92193
Wang, Cheng; Li, Xianyi
2014
Numerical solution of fourth-order time-fractional partial differential equations with variable coefficients. Zbl 1334.65179
2015
Global analysis for a delayed SIV model with direct and environmental transmissions. Zbl 1463.34339
Zhan, Tongqian; Meng, Xinzhu; Zhang, Tonghua
2016
Two CSCS-based iteration methods for solving absolute value equations. Zbl 1451.65058
Gu, Xian-Ming; Huang, Ting-Zhu; Li, Hou-Biao; Wang, Sheng-Feng; Li, Liang
2017
Global asymptotic stability of a generalized SIRS epidemic model with transfer from infectious to susceptible. Zbl 1459.34115
Bai, Yuzhen; Mu, Xiaoqing
2018
High-order copositive tensors and its applications. Zbl 1462.15029
Chen, Haibin; Wang, Yiju
2018
An iterative algorithm for solving a class of generalized coupled Sylvester-transpose matrix equations over bisymmetric or skew-anti-symmetric matrices. Zbl 1459.65054
Yan, Tongxin; Ma, Changfeng
2020
Finite-time synchronization for coupled systems with time delay and stochastic disturbance under feedback control. Zbl 1461.93458
Xu, Yao; Shen, Rong; Li, Wenxue
2020
Fractional order nonlinear mixed coupled systems with coupled integro-differential boundary conditions. Zbl 1468.34005
Ahmad, Bashir; Alsaedi, Ahmed; Ntouyas, Sotiris K.
2020
Polynomial and rational wave solutions of Kudryashov-Sinelshchikov equation and numerical simulations for its dynamic motions. Zbl 1461.35084
Ak, Turgut; Osman, Mohammed S.; Kara, Abdul Hamid
2020
Comparing the efficiency of Wolbachia driven Aedes mosquito suppression strategies. Zbl 1460.92203
Huang, Mugen; Hu, Linchao; Zheng, Bo
2019
Solitary wave solutions to the Tzitzeéica type equations obtained by a new efficient approach. Zbl 1461.35095
2019
Iterative method for a class of fourth-order $$p$$-Laplacian beam equation. Zbl 1458.34046
Bai, Zhanbing; Du, Zengji; Zhang, Shuo
2019
Existence of solutions for a one-dimensional Allen-Cahn equation. Zbl 1292.35154
Miranville, Alain
2013
Bogdanov-takens singularity in the comprehensive national power model with time delays. Zbl 1286.34111
Wang, Jingnan; Jiang, Weihua
2013
Existence of nonzero positive solutions of systems of second order elliptic boundary value problems. Zbl 1304.35272
Lan, Kunquan
2011
On the integrability of the differential systems in dimension two and of the polynomial differential systems in arbitrary dimension. Zbl 1304.34056
Llibre, Jaume
2011
Resonances of the SD oscillator due to the discontinuous phase. Zbl 1304.34070
Cao, Qingjie; Xiong, Yeping; Wiercigroch, Marian
2011
Nonlinear boundary conditions derived by singular pertubation in age structured population dynamics model. Zbl 1304.92109
Ducrot, Arnaud; Magal, Pierre; Seydi, Ousmane
2011
Existence of global solutions of multicomponent reactive transport problems with mass action kinetics in porous media. Zbl 1304.35555
Kräutle, Serge
2011
Existence and orbital stability of periodic wave solutions for the nonlinear Schrödinger equation. Zbl 1304.35633
Chen, Ai Yong; Wen, Shuangquan; Huang, Wentao
2012
A method for image encryption based on fractional-order hyperchaotic systems. Zbl 1355.68081
He, Jianbin; Yu, Simin; Cai, Jianping
2015
Counting spanning trees in prism and anti-prism graphs. Zbl 1463.05287
Sun, Weigang; Wang, Shuai; Zhang, Jingyuan
2016
Long time behavior of stochastic {MHD} equations perturbed by multiplicative noises. Zbl 1463.35094
Cui, Hongyong; Li, Yangrong; Yin, Jinyan
2016
Delay induced subcritical Hopf bifurcation in a diffusive predator-prey model with herd behavior and hyperbolic mortality. Zbl 1447.35039
Tang, Xiaosong; Jiang, Heping; Deng, Zhiyun; Yu, Tao
2017
A unified analysis of linear quaternion dynamic equations on time scales. Zbl 1459.34196
Cheng, Dong; Kou, Kit Ian; Xia, Yong Hui
2018
The geometrical analysis of a predator-prey model with multi-state dependent impulses. Zbl 1460.34061
Wang, Jianmei; Cheng, Huidong; Li, Yan; Zhang, Xiaoning
2018
Dynamics of a stochastic SIR model with both horizontal and vertical transmission. Zbl 1453.92312
Miao, Anqi; Zhang, Tongqian; Zhang, Jian; Wang, Chaoyang
2018
A compact difference scheme for fourth-order fractional sub-diffusion equations with Neumann boundary conditions. Zbl 1453.65237
Yao, Zhongsheng; Wang, Zhibo
2018
Operator splitting for numerical solutions of the RLW equation. Zbl 1455.65198
Yağmurlu, Nuri Murat; Uçar, Yusuf; Çelikkaya, İhsan
2018
A weak Galerkin finite element method for the second order elliptic problems with mixed boundary conditions. Zbl 1453.65408
Hussain, Saqib; Malluwawadu, Nolisa; Zhu, Peng
2018
Stability analysis and approximate solution of SIR epidemic model with Crowley-Martin type functional response and Holling type-II treatment rate by using homotopy analysis method. Zbl 1455.34039
2020
Higher-order models in phase separation. Zbl 1474.35377
Cherfils, Laurence; Miranville, Alain; Peng, Shuiran
2017
Limit cycle bifurcations in discontinuous planar systems with multiple lines. Zbl 1457.34050
Xiong, Yanqin; Han, Maoan
2020
Global dynamics of a Filippov plant disease model with an economic threshold of infected-susceptible ratio. Zbl 1460.92202
Huang, Lihong; Ma, Huili; Wang, Jiafu; Huang, Chuangxia
2020
Statistically localized sequences in metric spaces. Zbl 1471.40002
Nabiev, Anar Adiloglu; Savas, Ekrem; Gürdal, Mehmet
2019
Infinitely many solutions for fractional Schrödinger-Maxwell equations. Zbl 1465.35144
Xu, Jiafa; Wei, Zhongli; O’Regan, Donal; Cui, Yujun
2019
Successive iterations for unique positive solution of a nonlinear fractional $$q$$-integral boundary value problem. Zbl 1462.39008
Wang, Guotao; Bai, Zhanbing; Zhang, Lihong
2019
Positive solutions for a nonlinear discrete fractional boundary value problem with a $$p$$-Laplacian operator. Zbl 1464.39005
Cheng, Wei; Xu, Jiafa; O’Regan, Donal; Cui, Yujun
2019
Dynamic properties for nonlinear viscoelastic Kirchhoff-type equation with acoustic control boundary conditions II. Zbl 1461.35157
Li, Fushan; Xi, Shuai; Xu, Ke; Xue, Xiaomin
2019
Orbital stability of periodic traveling wave solutions to the generalized long-short wave equations. Zbl 1464.35305
Zheng, Xiaoxiao; Xin, Jie; Peng, Xiaoming
2019
Traveling wave solutions in coupled Chua’s circuits. I: Periodic solutions. Zbl 1307.34025
Chow, Shui-Nee; Jiang, Ming; Lin, Xiaobiao
2013
Global stability for a dynamic model of hepatitis B with antivirus treatment. Zbl 1298.35231
Huan, Qian; Ning, Peipei; Ding, Wei
2013
Exact explicit traveling wave solutions for a new coupled ZK system. Zbl 1304.74032
Wei, Minzhi; Tang, Shengqiang
2011
Stability of a cubic functional equation in fuzzy normed space. Zbl 1304.39034
Ravi, K.; Rassias, J.; Narasimman, P.
2011
Dynamic analysis of a fractional order phytoplankton model. Zbl 1297.26012
2013
Existence results for a new class of fractional impulsive partial neutral stochastic integro-differential equations with infinite delay. Zbl 1451.34100
Yan, Zuomao; Lu, Fangxia
2015
Random attractor for non-autonomous stochastic strongly damped wave equation on unbounded domains. Zbl 1451.37095
Wang, Zhaojuan; Zhou, Shengfan
2015
Stability results and existence theorems for nonlinear delay-fractional differential equations with $$\varphi_p^*$$-operator. Zbl 1464.34103
Khan, Hasib; Tunc, Cemil; Khan, Aziz
2020
A new iterative method for solving split feasibility problem. Zbl 07331945
Garodia, Chanchal; Uddin, Izhar
2020
Analysis of the time fractional nonlinear diffusion equation from diffusion process. Zbl 1480.35394
Liu, Jian-Gen; Yang, Xiao-Jun; Feng, Yi-Ying; Zhang, Hong-Yi
2020
An iterative algorithm for solving a class of generalized coupled Sylvester-transpose matrix equations over bisymmetric or skew-anti-symmetric matrices. Zbl 1459.65054
Yan, Tongxin; Ma, Changfeng
2020
Finite-time synchronization for coupled systems with time delay and stochastic disturbance under feedback control. Zbl 1461.93458
Xu, Yao; Shen, Rong; Li, Wenxue
2020
Fractional order nonlinear mixed coupled systems with coupled integro-differential boundary conditions. Zbl 1468.34005
Ahmad, Bashir; Alsaedi, Ahmed; Ntouyas, Sotiris K.
2020
Polynomial and rational wave solutions of Kudryashov-Sinelshchikov equation and numerical simulations for its dynamic motions. Zbl 1461.35084
Ak, Turgut; Osman, Mohammed S.; Kara, Abdul Hamid
2020
Stability analysis and approximate solution of SIR epidemic model with Crowley-Martin type functional response and Holling type-II treatment rate by using homotopy analysis method. Zbl 1455.34039
2020
Limit cycle bifurcations in discontinuous planar systems with multiple lines. Zbl 1457.34050
Xiong, Yanqin; Han, Maoan
2020
Global dynamics of a Filippov plant disease model with an economic threshold of infected-susceptible ratio. Zbl 1460.92202
Huang, Lihong; Ma, Huili; Wang, Jiafu; Huang, Chuangxia
2020
Further studies on limit cycle bifurcations for piecewise smooth near-Hamiltonian systems with multiple parameters. Zbl 1455.37045
Han, Maoan; Liu, Shanshan
2020
Landweber iterative method for an inverse source problem of time-fractional diffusion-wave equation on spherically symmetric domain. Zbl 1473.65174
Yang, Fan; Wang, Ni; Li, Xiao-Xiao
2020
Invariant measure and statistical solutions for non-autonomous discrete Klein-Gordon-Schrödinger-type equations. Zbl 1459.39021
Wu, Shang; Huang, Jianhua
2020
Dynamical behavior and solution of nonlinear difference equation via Fibonacci sequence. Zbl 1461.39001
Elsayed, Elsayed M.; Alzahrani, Faris; Abbas, Ibrahim; Alotaibi, N. H.
2020
Modelling and stability of epidemic model with free-living pathogens growing in the environment. Zbl 1460.92225
Xing, Yifan; Zhang, Liang; Wang, Xinghao
2020
Equivalent property of a more accurate half-discrete Hilbert’s inequality. Zbl 1457.26019
Wang, Aizhen; Yang, Bicheng
2020
Existence results of solutions for anti-periodic fractional Langevin equation. Zbl 07427160
Salem, Ahmed
2020
Positive periodic solution for second-order nonlinear differential equation with singularity of attractive type. Zbl 1455.34027
Liu, Jie; Cheng, Zhibo; Wang, Yi
2020
On a $$p$$-adic Hilbert-type integral operator and its applications. Zbl 07315440
Li, Huabing; Jin, Jianjun
2020
Flocking and collision avoidance of a cucker-Smale type system with singular weights. Zbl 1461.93019
Chen, Maoli; Li, Xiang; Wang, Xiao; Liu, Yicheng
2020
Spatial pattern formations in diffusive predator-prey systems with non-homogeneous Dirichlet boundary conditions. Zbl 1461.35042
Song, Yingwei; Zhang, Tie
2020
Survey on applications of semi-tensor product method in networked evolutionary games. Zbl 1460.91036
2020
Entire solutions of delay differential equations of Malmquist type. Zbl 1462.30056
Zhang, Ran-Ran; Huang, Zhi-Bo
2020
Existence and concentration result for Kirchhoff equations with critical exponent and Hartree nonlinearity. Zbl 1471.35019
Che, Guofeng; Chen, Haibo
2020
Further discussion on Kato’s chaos in set-valued discrete systems. Zbl 1483.37013
Li, Risong; Lu, Tianxiu; Chen, Guanrong; Yang, Xiaofang
2020
Existence and multiplicity of weak solutions for a class of fractional Sturm-Liouville boundary value problems with impulsive conditions. Zbl 1473.34006
Qiao, Yan; Chen, Fangqi; An, Yukun
2020
Self-adjoint realization of a class of third-order differential operators with an eigenparameter contained in the boundary conditions. Zbl 1473.34021
Li, Kun; Bai, Yulin; Wang, Wanyi; Meng, Fanwei
2020
Radial solution of asymptotically linear elliptic equation with mixed boundary value in annular domain. Zbl 1479.35470
Tian, Jian; Wei, Yuanhong
2020
Wong-Zakai approximations and attractors for fractional stochastic reaction-diffusion equations on unbounded domains. Zbl 1483.37096
Sun, Yaqing; Gao, Hongjun
2020
On the number of limit cycles by perturbing a piecewise smooth Hamilton system with two straight lines of separation. Zbl 1473.34025
Yang, Jihua
2020
Dynamic behavior of a delay cholera model with constant infectious period. Zbl 1458.92082
Zhou, Xue-Yong; Shi, Xiang-Yun; Cui, Jing-An
2020
Analysis of an HIV model with post-treatment control. Zbl 1458.92057
Wang, Shaoli; Xu, Fei
2020
Uniqueness of meromorphic functions concerning sharing two small functions with their derivatives. Zbl 1455.30027
Ma, Linke; Liu, Dan; Fang, Mingliang
2020
Asymptotic autonomy of random attractors for BBM equations with Laplace-multiplier noise. Zbl 1459.35047
Wang, Renhai; Li, Yangrong
2020
Qualitative analysis of a fourth order difference equation. Zbl 1458.39002
Alayachi, H. S.; Noorani, M. S. M.; Elsayed, E. M.
2020
Dynamics of an impulsive stochastic SIR epidemic model with saturated incidence rate. Zbl 1455.37071
Cao, Wenjie; Pan, Tao
2020
Bifurcation analysis and exact traveling wave solutions for a generic two-dimensional sine-Gordon equation in nonlinear optics. Zbl 1455.34044
Meng, Qing; He, Bin
2020
Beyond Sumudu transform and natural transform: $$\mathbb{J}$$-transform properties and applications. Zbl 1475.44001
Maitama, Shehu; Zhao, Weidong
2020
Modeling and dynamics of HIV transmission among high-risk groups in Guangzhou City, China. Zbl 1461.37081
Wu, Peng; Zhao, Hongyong
2020
Inverses and eigenpairs of tridiagonal Toeplitz matrix with opposite-bordered rows. Zbl 1458.15007
Fu, Yaru; Jiang, Xiaoyu; Jiang, Zhaolin; Jhang, Seongtae
2020
Dynamical behavior analysis of a two-dimensional discrete predator-prey model with prey refuge and fear factor. Zbl 1458.39009
Ma, Rui; Bai, Yuzhen; Wang, Fei
2020
Dynamical properties of a stochastic predator-prey model with functional response. Zbl 1456.92123
Lv, Jingliang; Zou, Xiaoling; Li, Yujie
2020
Global dynamics of a population model from river ecology. Zbl 1461.37078
Li, Keyu; Xu, Fangfang
2020
Exact peakon solutions given by the generalized hyperbolic functions for some nonlinear wave equations. Zbl 1459.35069
Li, Jibin; Han, Maoan
2020
Rough convergence of double sequences of fuzzy numbers. Zbl 1469.40010
2020
Existence and uniqueness of positive solution for nonlinear fractional $$q$$-difference equation with integral boundary conditions. Zbl 1462.39005
Guo, Caixia; Guo, Jianmin; Kang, Shugui; Li, Huapeng
2020
On inverses and eigenpairs of periodic tridiagonal Toeplitz matrices with perturbed corners. Zbl 1467.15003
Wei, Yunlan; Jiang, Xiaoyu; Jiang, Zhaolin; Shon, Sugoog
2020
Oscillation behavior of solution of impulsive fractional differential equation. Zbl 1457.34054
Feng, Limei; Han, Zhenlai
2020
Half-linear Volterra-Fredholm type integral inequalities on time scales and their applications. Zbl 1465.26021
Liu, Haidong
2020
Exact bound on the number of limit cycles arising from a periodic annulus bounded by a symmetric heteroclinic loop. Zbl 1457.34053
Sun, Xianbo
2020
Dynamics of a stochastic three species prey-predator model with intraguild predation. Zbl 1461.92090
Liu, Rong; Liu, Guirong
2020
On the strong convergence of a projection-based algorithm in Hilbert spaces. Zbl 1460.49006
Liu, Liya; Qin, Xiaolong
2020
The breather wave solutions, M-lump solutions and semi-rational solutions to a (2+1)-dimensional generalized Korteweg-de Vries equation. Zbl 1464.35292
Wang, Hui; Tian, Shou-Fu; Zhang, Tian-Tian; Chen, Yi
2020
Infinitely many solutions for critical fractional equation with sign-changing weight function. Zbl 1461.35209
Chen, Wei; Tang, Chun-Lei
2020
Finite iterative algorithm for the complex generalized Sylvester tensor equations. Zbl 07331944
Ke, Yifen
2020
Existence of positive solutions to a boundary value problem for a delayed singular high order fractional differential equation with sign-changing nonlinearity. Zbl 1465.34088
Liu, Dongyue; Zhang, Kemei
2020
Attractor for the non-autonomous long wave-short wave resonance interaction equation with damping. Zbl 1464.35300
Liu, Ranran; Liu, Hui; Xin, Jie
2020
Computation on the topological indices of hyaluronic acid. Zbl 1466.92292
Wang, Jiawei; Wang, Yiqiao; Wang, Ying; Zheng, Lina
2020
Compact finite difference schemes of the time fractional Black-Scholes model. Zbl 1461.91360
Tian, Zhaowei; Zhai, Shuying; Weng, Zhifeng
2020
Infinitely many solutions for a nonlocal problem. Zbl 1465.35216
Tang, Zhiyun; Ou, Zengqi
2020
Spatiotemporal dynamics in a predator-prey model with a functional response increasing in both predator and prey densities. Zbl 1461.92103
Yang, Ruizhi; Ding, Yuting
2020
Global analysis of the shadow Gierer-Meinhardt system with general linear boundary conditions in a random environment. Zbl 1466.60125
Antwi-Fordjour, Kwadwo; Kim, Seonguk; Nkashama, Marius
2020
Generalized p(x)-elliptic system with nonlinear physical data. Zbl 1465.35253
2020
Exponential attractor for Hindmarsh-Rose equations in neurodynamics. Zbl 1460.35049
Phan, Chi; You, Yuncheng
2020
A new third order exponentially fitted discretization for the solution of non-linear two point boundary value problems on a graded mesh. Zbl 07331977
Mohanty, R. K.; Manchanda, Geetan; Khurana, Gunjan; Khan, Arshad
2020
Global analysis for an epidemical model of vector-borne plant viruses with disease resistance and nonlinear incidence. Zbl 1460.92194
Fei, Lizhi; Zou, Lan; Chen, Xingwu
2020
Accelerated projection-based forward-backward splitting algorithms for monotone inclusion problems. Zbl 07331985
Tan, Bing; Zhou, Zheng; Qin, Xiaolong
2020
Remarks on the asymptotic behavior of scalar auxiliary variable (SAV) schemes for gradient-like flows. Zbl 1468.65135
Bouchriti, Anass; Pierre, Morgan; Alaa, Nour Eddine
2020
Global stability of autonomous and nonautonomous hepatitis B virus models in patchy environment. Zbl 1460.92208
Liu, Pengyan; Li, Hong-Xu
2020
Dynamics of a viral infectiology under treatment. Zbl 1460.92116
Ahmed, Shohel; Kamrujjaman, Md.; Rahman, Sumaiya
2020
Mixed monotone iterative technique for Hilfer fractional evolution equations with nonlocal conditions. Zbl 1468.34009
Gou, Haide; Li, Yongxiang; Li, Qixiang
2020
Turing-Hopf bifurcation in the reaction-diffusion system with delay and application to a diffusive predator-prey model. Zbl 1461.35035
Song, Yongli; Jiang, Heping; Yuan, Yuan
2019
A search for lump solutions to a combined fourth-order nonlinear PDE in (2+1)-dimensions. Zbl 1464.35287
Ma, Wen-Xiu
2019
Homoclinic solutions of discrete nonlinear systems via variational method. Zbl 1462.39003
Erbe, Lynn; Jia, Baoguo; Zhang, Qinqin
2019
Effect of herd shape in a diffusive predator-prey model with time delay. Zbl 1465.92147
Djilali, Salih
2019
Comparing the efficiency of Wolbachia driven Aedes mosquito suppression strategies. Zbl 1460.92203
Huang, Mugen; Hu, Linchao; Zheng, Bo
2019
Solitary wave solutions to the Tzitzeéica type equations obtained by a new efficient approach. Zbl 1461.35095
2019
Iterative method for a class of fourth-order $$p$$-Laplacian beam equation. Zbl 1458.34046
Bai, Zhanbing; Du, Zengji; Zhang, Shuo
2019
Statistically localized sequences in metric spaces. Zbl 1471.40002
Nabiev, Anar Adiloglu; Savas, Ekrem; Gürdal, Mehmet
2019
Infinitely many solutions for fractional Schrödinger-Maxwell equations. Zbl 1465.35144
Xu, Jiafa; Wei, Zhongli; O&rsquo;Regan, Donal; Cui, Yujun
2019
Successive iterations for unique positive solution of a nonlinear fractional $$q$$-integral boundary value problem. Zbl 1462.39008
Wang, Guotao; Bai, Zhanbing; Zhang, Lihong
2019
Positive solutions for a nonlinear discrete fractional boundary value problem with a $$p$$-Laplacian operator. Zbl 1464.39005
Cheng, Wei; Xu, Jiafa; O&rsquo;Regan, Donal; Cui, Yujun
2019
Dynamic properties for nonlinear viscoelastic Kirchhoff-type equation with acoustic control boundary conditions II. Zbl 1461.35157
Li, Fushan; Xi, Shuai; Xu, Ke; Xue, Xiaomin
2019
Orbital stability of periodic traveling wave solutions to the generalized long-short wave equations. Zbl 1464.35305
Zheng, Xiaoxiao; Xin, Jie; Peng, Xiaoming
2019
Bifurcations and chaos control in a discrete-time predator-prey system of Leslie type. Zbl 1470.92258
Rana, Sarker Md. Sohel
2019
Several types of periodic wave solutions and their relations of a Fujimoto-Watanabe equation. Zbl 1457.35061
Shi, Lijuan; Wen, Zhenshu
2019
Pullback attractors and invariant measures for the discrete Zakharov equations. Zbl 1462.37087
Zhu, Zeqi; Sang, Yanmiao; Zhao, Caidi
2019
On an extended Hardy-Hilbert’s inequality in the whole plane. Zbl 1457.26020
Yang, Bicheng; Huang, Meifa; Zhong, Yanru
2019
The revised generalized Tikhonov method for the backward time-fractional diffusion equation. Zbl 1461.35219
Deiveegan, Arumugam; Nieto, Juan J.; Prakash, Periasamy
2019
On the asymptotic solution to a type of piecewise-continuous second-order Dirichlet problems of Tikhonov system. Zbl 1461.93331
Qi, Xutian; Ni, Mingkang
2019
Multiple solutions for a nonhomogeneous Schrödinger-Poisson system with concave and convex nonlinearities. Zbl 1465.35183
Wang, Lixia; Ma, Shiwang
2019
Structural bifurcation of divergence-free vector fields near non-simple degenerate points with symmetry. Zbl 1464.35217
Deliceoglu, Ali; Bozkurt, Deniz
2019
Dynamics of a modified Leslie-Gower model with gestation effect and nonlinear harvesting. Zbl 1465.92099
Sivasamy, R.; Sathiyanathan, K.; Balachandran, K.
2019
Global dynamics of two phytoplankton-zooplankton models with toxic substances effect. Zbl 1465.92137
Chen, Shanshan; Yang, Hong; Wei, Junjie
2019
Multidimensional stability of planar waves for delayed reaction-diffusion equation with nonlocal diffusion. Zbl 1461.35091
Ma, Zhaohai; Wu, Xin; Yuan, Rong; Wang, Yang
2019
Properties of eigenvalues and spectral singularities for impulsive quadratic pencil of difference operators. Zbl 1462.39017
Bairamov, Elgiz; Cebesoy, Serifenur; Erdal, Ibrahim
2019
New predictor-corrector approach for nonlinear fractional differential equations: error analysis and stability. Zbl 1462.65078
2019
On an iterative method for a class of 2 point & 3 point nonlinear SBVPs. Zbl 1458.34050
Singh, Mandeep; Verma, Amit K.; Agarwal, Ravi P.
2019
Global behavior of a dynamic model with biodegradation of microcystins. Zbl 1461.92131
Song, Keying; Ma, Wanbiao; Guo, Ke
2019
Bogdanov-Takens bifurcation in a delayed Michaelis-Menten type ratio-dependent predator-prey system with prey harvesting. Zbl 1465.92086
Dai, Yunxian; Yang, Ping; Luo, Zhiliang; Lin, Yiping
2019
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### Cited by 2,069 Authors

 28 Han, Maoan 18 Shen, Wenxian 13 Yu, Pei 12 Qi, Feng 11 Miranville, Alain M. 11 Sun, Xianbo 10 Băleanu, Dumitru I. 10 Llibre, Jaume 10 Salako, Rachidi Bolaji 9 Chu, Yuming 8 Ahmad, Bashir 8 Giné, Jaume 8 Guo, Bai-Ni 8 Huo, Hai-Feng 8 Rezapour, Shahram 7 Liang, Xing 7 Qin, Xiaolong 7 Song, Yongli 7 Xia, Yonghui 7 Xiong, Yanqin 7 Yang, Junmin 7 Zhang, Tonghua 6 Agarwal, Ravi P. 6 Alquran, Marwan Taiseer 6 Al-saedi, Ahmed Eid Salem 6 Azroul, Elhoussine 6 Colli, Pierluigi 6 Dai, Binxiang 6 Du, Tingsong 6 Etemad, Sina 6 Hjiaj, Hassane 6 Khalique, Chaudry Masood 6 Li, Fushan 6 Li, Jibin 6 Liu, Xingbo 6 Meng, Xinzhu 6 Morita, Yoshihisa 6 Santra, Shyam Sundar 5 Ali, Muhammad Aamir 5 Benboubker, Mohamed Badr 5 Benchohra, Mouffak 5 Budak, Hüseyin 5 Ceng, Lu-Chuan 5 Chhatria, Gokula Nanda 5 Gilardi, Gianni 5 Grace, Said Rezk 5 Ilhan, Onur Alp 5 Mai, Ali 5 Manafian Heris, Jalil 5 Mishra, Lakshmi Narayan 5 Ntouyas, Sotiris K. 5 Sun, Guowei 5 Uddin, Izhar 5 Xiang, Hong 5 Yang, Jihua 5 Yu, Jian-She 5 Zhang, Lijun 5 Zhao, Liqin 4 Abbas, Said 4 Al-Taweel, Ahmed 4 Asheghi, Rasoul 4 Bao, Xiongxiong 4 Cai, Meilan 4 Chen, Yufu 4 Djilali, Salih 4 Fakih, Hussein 4 Ferčec, Brigita 4 Grasselli, Maurizio 4 Guo, Laigang 4 Guo, Zhiming 4 Huang, Wentao 4 Hussain, Saqib 4 Lan, Kunquan 4 Li, Feng 4 Li, Tatsien 4 Li, Wenxue 4 Li, Xianyi 4 Li, Zhong 4 Mishra, Vishnu Narayan 4 Nonlaopon, Kamsing 4 Ouaro, Stanislas 4 Rao, Bopeng 4 Shen, Zhongwei 4 Sprekels, Jürgen 4 Tripathy, Arun Kumar 4 Valls Anglés, Cláudia 4 Wang, Jiaxin 4 Wang, Jinfeng 4 Wang, Lin 4 Wang, Xiaoli 4 Xin, Yun 4 Xu, Wei 4 Yang, Bicheng 4 Yang, Qian 4 Yao, Jen-Chih 4 Zhang, Guohong 4 Zhang, Tongqian 3 Abbas, Mujahid 3 Aberqi, Ahmed 3 Al-Jammal, Hadeel ...and 1,969 more Authors
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### Cited in 251 Journals

 63 Journal of Applied Analysis and Computation 54 Advances in Difference Equations 52 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 35 AIMS Mathematics 32 Journal of Differential Equations 31 Physica A 25 Mathematical Biosciences and Engineering 24 Qualitative Theory of Dynamical Systems 23 Journal of Mathematical Analysis and Applications 23 Applied Mathematics and Computation 21 Discrete and Continuous Dynamical Systems. Series B 18 Boundary Value Problems 17 Journal of Inequalities and Applications 17 Nonlinear Analysis. Real World Applications 15 Journal of Computational and Applied Mathematics 15 Nonlinear Dynamics 15 Abstract and Applied Analysis 15 International Journal of Applied and Computational Mathematics 14 Chaos, Solitons and Fractals 14 Advances in Mathematical Physics 14 Journal of Function Spaces 13 Filomat 13 Journal of Applied Mathematics and Computing 12 Discrete and Continuous Dynamical Systems. Series S 12 International Journal of Biomathematics 11 Applicable Analysis 11 Mathematics and Computers in Simulation 11 Applied Mathematics Letters 9 Journal of the Franklin Institute 9 International Journal of Computer Mathematics 9 Computational and Applied Mathematics 9 Discrete and Continuous Dynamical Systems 9 Journal of Biological Dynamics 8 Applied Mathematics and Optimization 8 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 8 Applied Numerical Mathematics 8 South East Asian Journal of Mathematics and Mathematical Sciences 7 Mathematical Biosciences 7 Bulletin of Mathematical Biology 7 Journal of Dynamics and Differential Equations 7 International Journal of Nonlinear Sciences and Numerical Simulation 7 Mediterranean Journal of Mathematics 7 Open Mathematics 6 Journal of Mathematical Biology 6 Mathematica Slovaca 6 Asymptotic Analysis 6 Journal of Applied Mathematics 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Communications on Pure and Applied Analysis 6 Journal of Mathematical Inequalities 5 Computers & Mathematics with Applications 5 Journal of Geometry and Physics 5 Optimization 5 Fractals 5 Journal of Difference Equations and Applications 5 Discrete Dynamics in Nature and Society 5 Acta Mathematica Sinica. English Series 5 Nonlinear Analysis. Modelling and Control 5 Palestine Journal of Mathematics 5 Evolution Equations and Control Theory 5 Advances in Nonlinear Analysis 5 Journal of Mathematics 5 Journal of Applied Nonlinear Dynamics 4 International Journal of Control 4 Transactions of the American Mathematical Society 4 Acta Mathematica Universitatis Comenianae. New Series 4 Turkish Journal of Mathematics 4 Bulletin des Sciences Mathématiques 4 Complexity 4 Mathematical Problems in Engineering 4 Communications in Nonlinear Science and Numerical Simulation 4 Differential Equations 4 Acta Mathematica Scientia. Series B. (English Edition) 4 Stochastics and Dynamics 4 Differential Equations and Applications 4 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 4 Nonautonomous Dynamical Systems 4 Computational Methods for Differential Equations 3 Journal of Computational Physics 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 Acta Applicandae Mathematicae 3 Journal of the Nigerian Mathematical Society 3 Acta Mathematicae Applicatae Sinica. English Series 3 Journal of Scientific Computing 3 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 SIAM Journal on Mathematical Analysis 3 Expositiones Mathematicae 3 Topological Methods in Nonlinear Analysis 3 Differential Equations and Dynamical Systems 3 Nonlinear Functional Analysis and Applications 3 Journal of Evolution Equations 3 Acta Mathematica Scientia. Series A. (Chinese Edition) 3 SIAM Journal on Applied Dynamical Systems 3 Complex Variables and Elliptic Equations 3 Applicable Analysis and Discrete Mathematics 3 Analysis and Mathematical Physics 3 Afrika Matematika 3 Journal of Mathematical Extension 3 Journal of Elliptic and Parabolic Equations 3 Electronic Research Archive ...and 151 more Journals
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### Cited in 47 Fields

 436 Ordinary differential equations (34-XX) 422 Partial differential equations (35-XX) 258 Biology and other natural sciences (92-XX) 163 Dynamical systems and ergodic theory (37-XX) 143 Numerical analysis (65-XX) 106 Real functions (26-XX) 105 Operator theory (47-XX) 54 Fluid mechanics (76-XX) 53 Difference and functional equations (39-XX) 51 Systems theory; control (93-XX) 42 Statistical mechanics, structure of matter (82-XX) 40 Integral equations (45-XX) 37 Probability theory and stochastic processes (60-XX) 23 Calculus of variations and optimal control; optimization (49-XX) 23 Mechanics of deformable solids (74-XX) 23 Operations research, mathematical programming (90-XX) 21 Special functions (33-XX) 21 General topology (54-XX) 20 Linear and multilinear algebra; matrix theory (15-XX) 19 Combinatorics (05-XX) 15 Classical thermodynamics, heat transfer (80-XX) 13 Number theory (11-XX) 13 Functional analysis (46-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 12 Information and communication theory, circuits (94-XX) 11 Global analysis, analysis on manifolds (58-XX) 9 Functions of a complex variable (30-XX) 9 Approximations and expansions (41-XX) 9 Integral transforms, operational calculus (44-XX) 9 Computer science (68-XX) 9 Mechanics of particles and systems (70-XX) 7 Sequences, series, summability (40-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 5 Optics, electromagnetic theory (78-XX) 5 Quantum theory (81-XX) 4 Potential theory (31-XX) 3 Measure and integration (28-XX) 2 Field theory and polynomials (12-XX) 2 Statistics (62-XX) 1 General and overarching topics; collections (00-XX) 1 Mathematical logic and foundations (03-XX) 1 Commutative algebra (13-XX) 1 Algebraic geometry (14-XX) 1 Nonassociative rings and algebras (17-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Abstract harmonic analysis (43-XX)