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Lu, Haishen

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Author ID: lu.haishen Recent zbMATH articles by "Lu, Haishen"
Published as: Lü, Haishen; Lu, H.; Lü, H.; Lu, Haishen; Lü, Hai-shen; Lu, H.-S.
Documents Indexed: 64 Publications since 1992
all top 5

Serials

4 Applied Mathematics and Computation
3 Annals of Differential Equations
3 Memoirs on Differential Equations and Mathematical Physics
2 Indian Journal of Pure & Applied Mathematics
2 Journal of Applied Mechanics
2 Journal of Mathematical Analysis and Applications
2 Journal of Computational and Applied Mathematics
2 Zeitschrift für Analysis und ihre Anwendungen
2 Applied Mathematics Letters
2 Mathematica Applicata
2 Applications of Mathematics
2 Mathematical Inequalities & Applications
2 Journal of High Energy Physics
1 Modern Physics Letters A
1 Applicable Analysis
1 Classical and Quantum Gravity
1 Houston Journal of Mathematics
1 Nuclear Physics. B
1 Physics Letters. B
1 Canadian Journal of Mathematics
1 Glasgow Mathematical Journal
1 Mathematika
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Studia Scientiarum Mathematicarum Hungarica
1 Journal of Mathematics. Wuhan University
1 Journal of Lanzhou University. Natural Sciences
1 Acta Mathematica Hungarica
1 Applied Numerical Mathematics
1 Journal of Applied Mathematics and Stochastic Analysis
1 Glasnik Matematički. Serija III
1 Communications in Numerical Methods in Engineering
1 Electronic Journal of Differential Equations (EJDE)
1 Methods and Applications of Analysis
1 Pure and Applied Mathematics
1 Journal of Difference Equations and Applications
1 Journal of Applied Analysis
1 Soft Computing
1 Journal of Applied Statistics
1 Neliniĭni Kolyvannya
1 European Journal of Mechanics. A. Solids
1 European Journal of Mechanics. B. Fluids
1 Acta Analysis Functionalis Applicata. AAFA
1 Nonlinear Analysis. Real World Applications
1 Nonlinear Functional Analysis and Applications
1 Advances in Difference Equations
1 Boundary Value Problems

Publications by Year

Citations contained in zbMATH Open

40 Publications have been cited 779 times in 673 Documents Cited by Year
Positive solutions for boundary value problem of nonlinear fractional differential equation. Zbl 1079.34048
Bai, Zhanbing; Lü, Haishen
492
2005
Eigenvalues and the one-dimensional \(p\)-Laplacian. Zbl 1002.34019
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
73
2002
Multiple positive solutions for the one-dimensional singular \(p\)-Laplacian. Zbl 1048.34047
Lü, Haishen; O’Regan, Donal; Zhong, Chengkui
31
2002
Existence theorems for the one-dimensional singular \(p\)-Laplacian equation with sign changing nonlinearities. Zbl 1031.34023
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
29
2003
A note on singular nonlinear boundary value problems for the one-dimensional \(p\)-Laplacian. Zbl 0981.34013
Lü, Haishen; Zhong, Chengkui
18
2001
Charged dilatonic AdS black holes and magnetic \(\mathrm{AdS}_{D-2}\times R^2\) vacua. Zbl 1342.83493
Lü, H.
13
2013
Multiplicity of positive solutions for a \((p_1,p_2)\)-Laplacian system and its applications. Zbl 1272.34031
Cheng, Xiyou; Lü, Haishen
12
2012
Positive solutions for singular \(p\)-Laplacian equations with sign changing nonlinearities using inequality theory. Zbl 1071.34018
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
10
2005
Existence theorems for the one-dimensional singular \(p\)-Laplacian equation with a nonlinear boundary condition. Zbl 1071.34019
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
10
2005
Exact black hole formation in asymptotically (A)ds and flat spacetimes. Zbl 1317.83057
Zhang, Xuefeng; Lü, H.
9
2014
Upper and lower solutions for the singular \(p\)-Laplacian with sign changing nonlinearities and nonlinear boundary data. Zbl 1082.34022
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
6
2005
\(\mathrm{SL}(n,\mathbb R)\)-Toda black holes. Zbl 1284.83090
Lü, H.; Yang, Wei
6
2013
On the existence of multiple periodic solutions for the vector \(p\)-Laplacian via critical point theory. Zbl 1099.34021
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
6
2005
High-order discontinuous Galerkin method for elastohydrodynamic lubrication line contact problems. Zbl 1077.76045
Lu, H.; Berzins, M.; Goodyer, C. E.; Jimack, P. K.
5
2005
Positive radial solutions of a singular elliptic equation with sign changing nonlinearities. Zbl 1147.34015
Lü, Haishen; Bai, Zhanbing
5
2006
Nonuniform nonresonance at the first eigenvalue of the one-dimensional singular \(p\)-Laplacian. Zbl 1076.34019
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
4
2005
Positive radial solutions for a quasilinear system. Zbl 1100.34018
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
4
2006
Existence and multiplicity of positive solutions for singular semipositone \(p\)-Laplacian equations. Zbl 1122.34014
Agarwal, Ravi P.; Cao, Daomin; Lü, Haishen; O’Regan, Donal
4
2006
An upper and lower solution method for the one-dimensional singular \(p\)-Laplacian. Zbl 1052.34020
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
4
2003
Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach. Zbl 1164.34351
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
4
2007
Positive solutions for the singular \(p\)-Laplace equation. Zbl 1102.34013
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
3
2005
A positive solution for singular discrete boundary value problems with sign-changing nonlinearities. Zbl 1099.39008
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
3
2006
A necessary and sufficient condition for the existence of positive solutions to the singular \(p\)-Laplacian. Zbl 1048.34040
Agarwal, R. P.; Lü, Haishen; O’Regan, D.
3
2003
Positive solutions for the boundary value problem \((| u''|^{p-2} u'')''-\lambda q(t) f(u(t))= 0\). Zbl 1161.34315
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
3
2003
Existence of positive solutions for the one-dimension singular \(P\)-laplacian equation with sign changing nonlinearities via the method of upper and lower solution. Zbl 1079.34511
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
2
2003
Asymptotic structure of Einstein-Maxwell-dilaton theory and its five dimensional origin. Zbl 1429.83016
Lü, H.; Mao, Pujian; Wu, Jun-Bao
2
2019
Positive solutions for singular nonlinear beam equation. Zbl 1122.34306
Song, Ruhao; Lü, Haishen
2
2007
Triple solutions for the one-dimensional \(p\)-Laplacian. Zbl 1056.34026
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
2
2003
A general existence theorem for the singular equation \((\varphi_p(y'))'+f(t,y)=0\). Zbl 1003.34017
Lü, Haishen; O’Regan, Donal
2
2002
An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing nonlinearities. Zbl 1140.34327
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
2
2008
Construction of upper and lower solutions for singular discrete initial and boundary value problems via inequality theory. Zbl 1103.39021
Lü, Haishen; O’Regan, Donal
1
2005
Positive solutions for Dirichlet problems of singular quasilinear elliptic equations via variational methods. Zbl 1281.35033
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
1
2004
An eigenvalue interval of solutions for a singular discrete boundary value problem with sign changing nonlinearities. Zbl 1127.39035
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
1
2006
Finite volume methods for multiphysics problems. Zbl 1052.80513
Bailey, C.; Cross, M.; Pericleous, K.; Taylor, G. A.; Croft, N.; Wheeler, D.; Lu, H.
1
1999
Fuzzy system and CMAC network with B-spline membership/basis functions are smooth approximators. Zbl 1063.93029
Wang, S.; Lu, H.
1
2003
A general existence theorem for positive solutions to singular second order ordinary and functional differential equations. Zbl 0979.34013
Lü, Haishen; O’Regan, Donal
1
2000
Existence theorems for three-point boundary value problem. Zbl 0994.34009
Lü, Haishen; Zhong, Chengkui
1
2001
Existence and multiplicity of positive solutions for singular \(p\)-Laplacian equations. Zbl 1135.35025
Lü, Haishen; Xie, Yi
1
2007
Dynamic steady-state stress field in a web during slitting. Zbl 1111.74522
Liu, C.; Lu, H.; Huang, Y.
1
2005
Positive solutions for non-resonant singular boundary-value problems with a linear term. Zbl 1128.34012
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
1
2007
Asymptotic structure of Einstein-Maxwell-dilaton theory and its five dimensional origin. Zbl 1429.83016
Lü, H.; Mao, Pujian; Wu, Jun-Bao
2
2019
Exact black hole formation in asymptotically (A)ds and flat spacetimes. Zbl 1317.83057
Zhang, Xuefeng; Lü, H.
9
2014
Charged dilatonic AdS black holes and magnetic \(\mathrm{AdS}_{D-2}\times R^2\) vacua. Zbl 1342.83493
Lü, H.
13
2013
\(\mathrm{SL}(n,\mathbb R)\)-Toda black holes. Zbl 1284.83090
Lü, H.; Yang, Wei
6
2013
Multiplicity of positive solutions for a \((p_1,p_2)\)-Laplacian system and its applications. Zbl 1272.34031
Cheng, Xiyou; Lü, Haishen
12
2012
An approximation approach to eigenvalue intervals for singular boundary value problems with sign changing nonlinearities. Zbl 1140.34327
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
2
2008
Existence to singular boundary value problems with sign changing nonlinearities using an approximation method approach. Zbl 1164.34351
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
4
2007
Positive solutions for singular nonlinear beam equation. Zbl 1122.34306
Song, Ruhao; Lü, Haishen
2
2007
Existence and multiplicity of positive solutions for singular \(p\)-Laplacian equations. Zbl 1135.35025
Lü, Haishen; Xie, Yi
1
2007
Positive solutions for non-resonant singular boundary-value problems with a linear term. Zbl 1128.34012
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
1
2007
Positive radial solutions of a singular elliptic equation with sign changing nonlinearities. Zbl 1147.34015
Lü, Haishen; Bai, Zhanbing
5
2006
Positive radial solutions for a quasilinear system. Zbl 1100.34018
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
4
2006
Existence and multiplicity of positive solutions for singular semipositone \(p\)-Laplacian equations. Zbl 1122.34014
Agarwal, Ravi P.; Cao, Daomin; Lü, Haishen; O’Regan, Donal
4
2006
A positive solution for singular discrete boundary value problems with sign-changing nonlinearities. Zbl 1099.39008
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
3
2006
An eigenvalue interval of solutions for a singular discrete boundary value problem with sign changing nonlinearities. Zbl 1127.39035
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
1
2006
Positive solutions for boundary value problem of nonlinear fractional differential equation. Zbl 1079.34048
Bai, Zhanbing; Lü, Haishen
492
2005
Positive solutions for singular \(p\)-Laplacian equations with sign changing nonlinearities using inequality theory. Zbl 1071.34018
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
10
2005
Existence theorems for the one-dimensional singular \(p\)-Laplacian equation with a nonlinear boundary condition. Zbl 1071.34019
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
10
2005
Upper and lower solutions for the singular \(p\)-Laplacian with sign changing nonlinearities and nonlinear boundary data. Zbl 1082.34022
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
6
2005
On the existence of multiple periodic solutions for the vector \(p\)-Laplacian via critical point theory. Zbl 1099.34021
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
6
2005
High-order discontinuous Galerkin method for elastohydrodynamic lubrication line contact problems. Zbl 1077.76045
Lu, H.; Berzins, M.; Goodyer, C. E.; Jimack, P. K.
5
2005
Nonuniform nonresonance at the first eigenvalue of the one-dimensional singular \(p\)-Laplacian. Zbl 1076.34019
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
4
2005
Positive solutions for the singular \(p\)-Laplace equation. Zbl 1102.34013
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
3
2005
Construction of upper and lower solutions for singular discrete initial and boundary value problems via inequality theory. Zbl 1103.39021
Lü, Haishen; O’Regan, Donal
1
2005
Dynamic steady-state stress field in a web during slitting. Zbl 1111.74522
Liu, C.; Lu, H.; Huang, Y.
1
2005
Positive solutions for Dirichlet problems of singular quasilinear elliptic equations via variational methods. Zbl 1281.35033
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
1
2004
Existence theorems for the one-dimensional singular \(p\)-Laplacian equation with sign changing nonlinearities. Zbl 1031.34023
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
29
2003
An upper and lower solution method for the one-dimensional singular \(p\)-Laplacian. Zbl 1052.34020
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
4
2003
A necessary and sufficient condition for the existence of positive solutions to the singular \(p\)-Laplacian. Zbl 1048.34040
Agarwal, R. P.; Lü, Haishen; O’Regan, D.
3
2003
Positive solutions for the boundary value problem \((| u''|^{p-2} u'')''-\lambda q(t) f(u(t))= 0\). Zbl 1161.34315
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
3
2003
Existence of positive solutions for the one-dimension singular \(P\)-laplacian equation with sign changing nonlinearities via the method of upper and lower solution. Zbl 1079.34511
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
2
2003
Triple solutions for the one-dimensional \(p\)-Laplacian. Zbl 1056.34026
Lü, Haishen; O’Regan, Donal; Agarwal, Ravi P.
2
2003
Fuzzy system and CMAC network with B-spline membership/basis functions are smooth approximators. Zbl 1063.93029
Wang, S.; Lu, H.
1
2003
Eigenvalues and the one-dimensional \(p\)-Laplacian. Zbl 1002.34019
Agarwal, Ravi P.; Lü, Haishen; O’Regan, Donal
73
2002
Multiple positive solutions for the one-dimensional singular \(p\)-Laplacian. Zbl 1048.34047
Lü, Haishen; O’Regan, Donal; Zhong, Chengkui
31
2002
A general existence theorem for the singular equation \((\varphi_p(y'))'+f(t,y)=0\). Zbl 1003.34017
Lü, Haishen; O’Regan, Donal
2
2002
A note on singular nonlinear boundary value problems for the one-dimensional \(p\)-Laplacian. Zbl 0981.34013
Lü, Haishen; Zhong, Chengkui
18
2001
Existence theorems for three-point boundary value problem. Zbl 0994.34009
Lü, Haishen; Zhong, Chengkui
1
2001
A general existence theorem for positive solutions to singular second order ordinary and functional differential equations. Zbl 0979.34013
Lü, Haishen; O’Regan, Donal
1
2000
Finite volume methods for multiphysics problems. Zbl 1052.80513
Bailey, C.; Cross, M.; Pericleous, K.; Taylor, G. A.; Croft, N.; Wheeler, D.; Lu, H.
1
1999
all top 5

Cited by 729 Authors

27 Ge, Weigao
26 Liu, Wenbin
21 Sun, Shurong
19 Bai, Zhanbing
19 Han, Zhenlai
19 O’Regan, Donal
18 Lee, Yong-Hoon Lee
15 Liu, Lishan
14 Wu, Yonghong
13 Agarwal, Ravi P.
13 Goodrich, Christopher S.
11 Kong, Lingju
11 Zhao, Yige
10 Feng, Meiqiang
10 Graef, John R.
10 Mâagli, Habib
9 Ahmad, Bashir
9 Chen, Taiyong
9 Hu, Zhigang
8 Khan, Rahmat Ali
8 Liang, Sihua
8 Sim, Inbo
8 Xu, Jiafa
8 Xu, XiangHui
8 Zhou, Wenxue
7 Băleanu, Dumitru I.
7 Henderson, Johnny Lee
7 Jiang, Daqing
7 Liu, Xiping
7 Lu, Haishen
7 Ma, Dexiang
7 Sadarangani, Kishin B.
7 Shah, Kamal
7 Su, Youhui
7 Sun, Hongrui
7 Tian, Yuansheng
7 Zhang, Jihui
7 Zhang, Xingqiu
7 Zhang, Xinguang
6 Bachar, Imed
6 Chen, Yi
6 Harjani, Jackie
6 He, Zhimin
6 Jia, Mei
6 Ntouyas, Sotiris K.
6 Rezapour, Shahram
6 Wang, Guotao
6 Yuan, Chengjun
6 Zhang, Ziheng
5 Cabada, Alberto
5 Chen, Anping
5 El Abidine, Zagharide Zine
5 Feng, Hanying
5 Han, Xiaoling
5 Jiang, Weihua
5 Kim, Chan-Gyun
5 Li, Wan-Tong
5 Li, Yongxiang
5 Papageorgiou, Nikolaos S.
5 Prasad, Kapula Rajendra
5 Staněk, Svatoslav
5 Tang, Xianhua
5 Wang, Min
5 Zhang, Shuqin
5 Zhao, Xiangkui
4 Bai, Chuanzhi
4 Caballero, Josefa
4 de la Sen, Manuel
4 Gou, Haide
4 Ji, Dehong
4 Jiang, Jiqiang
4 Krushna, Boddu Muralee Bala
4 Lee, Eunkyoung
4 Li, Qiuping
4 Liu, Jiaying
4 Liu, Zhenhai
4 Nieto Roig, Juan Jose
4 Orpel, Aleksandra
4 Ouahab, Abdelghani
4 Salem, Hussein A. H.
4 Su, Xinwei
4 Tang, Xiaosong
4 Toumi, Faten
4 Ur Rehman, Mujeeb
4 Wang, Jinhua
4 Wang, Yongqing
4 Wang, Youyu
4 Wei, Zhongli
4 Xiang, Hongjun
4 Xu, Xiaojie
4 Yan, Rian
4 Zhang, Yinghan
4 Zou, Yumei
3 Ben Othman, Sonia
3 Benhassine, Abderrazek
3 Boulaaras, Salah Mahmoud
3 Cabrera, Ignacio José
3 Chai, Guoqing
3 Chen, Haibo
3 Chu, Jifeng
...and 629 more Authors
all top 5

Cited in 123 Serials

76 Advances in Difference Equations
60 Abstract and Applied Analysis
49 Boundary Value Problems
41 Computers & Mathematics with Applications
40 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
34 Journal of Applied Mathematics and Computing
29 Applied Mathematics and Computation
25 Journal of Mathematical Analysis and Applications
16 Discrete Dynamics in Nature and Society
14 Applied Mathematics Letters
14 Fractional Calculus & Applied Analysis
11 Mediterranean Journal of Mathematics
11 Journal of Function Spaces
10 Applicable Analysis
10 Journal of Computational and Applied Mathematics
9 Mathematical Methods in the Applied Sciences
9 Nonlinear Analysis. Modelling and Control
8 Communications in Nonlinear Science and Numerical Simulation
7 Mathematical and Computer Modelling
7 International Journal of Differential Equations
7 Fractional Differential Calculus
6 Positivity
6 Journal of Nonlinear Science and Applications
6 International Journal of Applied and Computational Mathematics
5 Journal of Differential Equations
5 Journal of Difference Equations and Applications
5 Mathematical Problems in Engineering
5 Differential Equations and Dynamical Systems
5 Journal of Applied Mathematics
5 Journal of Function Spaces and Applications
4 Bulletin of the Malaysian Mathematical Sciences Society. Second Series
4 ISRN Mathematical Analysis
4 Journal of Applied Analysis and Computation
3 Rocky Mountain Journal of Mathematics
3 Zeitschrift für Analysis und ihre Anwendungen
3 Journal of Inequalities and Applications
3 Journal of Fixed Point Theory and Applications
2 Lithuanian Mathematical Journal
2 Ukrainian Mathematical Journal
2 Proceedings of the American Mathematical Society
2 Ricerche di Matematica
2 Acta Applicandae Mathematicae
2 Acta Mathematicae Applicatae Sinica. English Series
2 Applications of Mathematics
2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
2 Applied Mathematics. Series B (English Edition)
2 Electronic Journal of Differential Equations (EJDE)
2 Filomat
2 Complexity
2 Arab Journal of Mathematical Sciences
2 Acta Mathematica Sinica. English Series
2 Boletim da Sociedade Paranaense de Matemática. Terceira Série
2 Fixed Point Theory and Applications
2 Communications in Mathematical Analysis
2 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche
2 International Journal of Biomathematics
2 Advances in Pure and Applied Mathematics
2 Journal of Pseudo-Differential Operators and Applications
2 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM
2 Analysis and Mathematical Physics
2 Mathematical Sciences
2 Advances in Nonlinear Analysis
2 Journal of Elliptic and Parabolic Equations
1 Bulletin of the Australian Mathematical Society
1 Indian Journal of Pure & Applied Mathematics
1 Mathematical Notes
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
1 Czechoslovak Mathematical Journal
1 Demonstratio Mathematica
1 Glasgow Mathematical Journal
1 International Journal of Mathematics and Mathematical Sciences
1 Journal of the Korean Mathematical Society
1 Journal of Optimization Theory and Applications
1 Kyungpook Mathematical Journal
1 Mathematische Nachrichten
1 Mathematica Slovaca
1 Monatshefte für Mathematik
1 Numerical Functional Analysis and Optimization
1 Results in Mathematics
1 Bulletin of the Korean Mathematical Society
1 Applied Mathematics and Mechanics. (English Edition)
1 Chinese Annals of Mathematics. Series B
1 Acta Mathematica Hungarica
1 International Journal of Mathematics
1 Numerical Algorithms
1 International Journal of Computer Mathematics
1 Set-Valued Analysis
1 The Journal of Analysis
1 Russian Journal of Mathematical Physics
1 Computational and Applied Mathematics
1 Acta Universitatis Matthiae Belii. Series Mathematics
1 Georgian Mathematical Journal
1 Bulletin des Sciences Mathématiques
1 Opuscula Mathematica
1 Taiwanese Journal of Mathematics
1 Novi Sad Journal of Mathematics
1 European Journal of Mechanics. A. Solids
1 Communications in Contemporary Mathematics
1 Annales Henri Poincaré
...and 23 more Serials

Citations by Year