## Erbe, Lynn Harry

Compute Distance To:
 Author ID: erbe.lynn-h Published as: Erbe, Lynn; Erbe, L. H.; Erbe, L.; Erbe, Lynn H. more...less External Links: MGP
 Documents Indexed: 249 Publications since 1969, including 1 Book 9 Contributions as Editor Reviewing Activity: 2 Reviews Biographic References: 1 Publication Co-Authors: 66 Co-Authors with 215 Joint Publications 2,101 Co-Co-Authors
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### Co-Authors

 37 single-authored 85 Peterson, Allan C. 29 Jia, Baoguo 15 Baoguo, Jia 14 Krawcewicz, Wieslaw Z. 12 Butler, Geoffrey J. 12 Kong, Qingkai 10 Freedman, Herbert Irving 10 Hassan, Taher S. 10 Liu, Xinzhi 10 Saker, Samir H. 9 Mert, Raziye 7 Rao, Vadrevu Sree Hari 7 Wu, Jianhong 7 Zhang, Binggen 6 Wu, Hongwu 5 Guo, Dajun 5 Liu, Xiang 5 Yan, Pengxiang 4 Chen, Shaozhu 4 Du, Feifei 4 Mathsen, Ronald M. 4 Tang, Moxun 4 Tisdell, Christopher C. 3 Goodrich, Christopher S. 3 Hu, Shouchuan 3 Liang, Zhongchao 3 Palamides, Panos K. 3 Schmitt, Klaus 3 Wang, Haiyan 2 Akin, Elvan 2 Bohner, Martin J. 2 Chen, Churong 2 Gęba, Kazimierz 2 Knobloch, Hans-Wilhelm 2 Muldowney, James S. 2 Mysore, S. 2 Oganesyan, Gro R. 2 Ou, Boqun 2 Řehák, Pavel 2 Xu, Zhiting 2 Yu, Jian-She 1 Allegretto, Walter 1 Anderson, Douglas Robert 1 Bullock, John D. 1 Chen, Siyuan 1 Davis, John M. 1 Gensler, Scott 1 Henderson, Johnny Lee 1 Hilger, Stefan 1 Hu, Wei 1 Huang, Qingguang 1 Kaymakçalan, Billur 1 Kong, Lingju 1 Li, Longtu 1 Ma, Ruyun 1 Mingarelli, Angelo B. 1 Peschke, Georg 1 Ruan, Shigui 1 Seshagiri Rao, K. V. V. 1 Tran, Hoainam 1 Wang, Zhi-Cheng 1 Wong, Patricia J. Y. 1 Xu, Yuantong 1 Yang, Qiaoshun 1 Zafer, Ağacık 1 Zhang, Qinqin
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### Serials

 18 Journal of Difference Equations and Applications 16 Journal of Mathematical Analysis and Applications 11 Rocky Mountain Journal of Mathematics 11 Proceedings of the American Mathematical Society 10 The Canadian Applied Mathematics Quarterly 8 Applied Mathematics and Computation 8 Canadian Mathematical Bulletin 7 Dynamic Systems and Applications 7 Differential Equations and Dynamical Systems 7 Nonlinear Analysis. Theory, Methods & Applications 6 Annali di Matematica Pura ed Applicata. Serie Quarta 6 Journal of Differential Equations 5 Applicable Analysis 5 Journal of Computational and Applied Mathematics 5 Pacific Journal of Mathematics 5 Differential and Integral Equations 5 SIAM Journal on Mathematical Analysis 4 Computers & Mathematics with Applications 4 Annales Polonici Mathematici 4 Electronic Journal of Differential Equations (EJDE) 4 Communications in Applied Analysis 3 Bulletin of the Australian Mathematical Society 3 Funkcialaj Ekvacioj. Serio Internacia 3 Hiroshima Mathematical Journal 3 Applied Mathematics Letters 3 Mathematical and Computer Modelling 3 Electronic Journal of Qualitative Theory of Differential Equations 3 Advances in Difference Equations 2 Journal of the Australian Mathematical Society, Series B 2 Journal of Mathematical and Physical Sciences 2 Canadian Journal of Mathematics 2 Czechoslovak Mathematical Journal 2 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 2 Transactions of the American Mathematical Society 2 Utilitas Mathematica 2 Journal of Integral Equations and Applications 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Turkish Journal of Mathematics 2 Mathematical Inequalities & Applications 2 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 2 Nonlinear Dynamics and Systems Theory 2 Journal of Applied Analysis and Computation 1 Mathematical Biosciences 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 ZAMP. Zeitschrift für angewandte Mathematik und Physik 1 Bulletin of Mathematical Biology 1 Archiv der Mathematik 1 Chinese Journal of Mathematics 1 Indian Journal of Mathematics 1 Journal of Approximation Theory 1 Journal of the London Mathematical Society. Second Series 1 Mathematische Nachrichten 1 Mathematica Slovaca 1 Mathematische Zeitschrift 1 Results in Mathematics 1 Journal of Applied Mathematics and Stochastic Analysis 1 Bulletin of the Allahabad Mathematical Society 1 Panamerican Mathematical Journal 1 Bulletin de la Société Mathématique de Belgique. Série A 1 Georgian Mathematical Journal 1 Filomat 1 ETNA. Electronic Transactions on Numerical Analysis 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 Abstract and Applied Analysis 1 Journal of Inequalities and Applications 1 Acta Mathematica Sinica. English Series 1 Journal of Applied Mathematics and Computing 1 Mediterranean Journal of Mathematics 1 Pure and Applied Mathematics, Marcel Dekker 1 Applicable Analysis and Discrete Mathematics
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### Fields

 193 Ordinary differential equations (34-XX) 77 Difference and functional equations (39-XX) 17 Real functions (26-XX) 14 Partial differential equations (35-XX) 10 Integral equations (45-XX) 10 Biology and other natural sciences (92-XX) 9 General and overarching topics; collections (00-XX) 7 Operator theory (47-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 General topology (54-XX) 3 Systems theory; control (93-XX) 2 Special functions (33-XX) 2 Functional analysis (46-XX) 2 Algebraic topology (55-XX) 2 Numerical analysis (65-XX) 1 History and biography (01-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX)

### Citations contained in zbMATH Open

209 Publications have been cited 3,576 times in 2,200 Documents Cited by Year
On the existence of positive solutions of ordinary differential equations. Zbl 0802.34018
Erbe, L. H.; Wang, Haiyan
1994
Multiple positive solutions of some boundary value problems. Zbl 0805.34021
Erbe, L. H.; Hu, Shouchuan; Wang, Haiyan
1994
Oscillation theory for functional differential equations. Zbl 0821.34067
Erbe, L. H.; Kong, Qingkai; Zhang, B. G.
1994
Positive solutions for a nonlinear differential equation on a measure chain. Zbl 0963.34020
Erbe, L.; Peterson, A.
2000
Oscillation of discrete analogues of delay equations. Zbl 0723.39004
Erbe, L. H.; Zhang, B. G.
1989
Oscillation criteria for second-order nonlinear delay dynamic equations. Zbl 1125.34046
Erbe, L.; Peterson, A.; Saker, S. H.
2007
Oscillation criteria for second-order nonlinear dynamic equations on time scales. Zbl 1050.34042
Erbe, Lynn; Peterson, Allan; Saker, S. H.
2003
Comparison principles for impulsive parabolic equations with applications to models of single species growth. Zbl 0881.35006
Erbe, L. H.; Freedman, H. I.; Liu, X. Z.; Wu, Jianhong
1991
Sturmian theory on measure chains. Zbl 0868.39007
Erbe, Lynn; Hilger, Stefan
1993
Green’s functions and comparison theorems for differential equations on measure chains. Zbl 0938.34027
Erbe, Lynn; Peterson, Allan
1999
Global stability of a linear nonautonomous delay difference equation. Zbl 0855.39007
Erbe, L. H.; Xia, H.
1995
Riccati techniques and variational principles in oscillation theory for linear systems. Zbl 0648.34031
Butler, G. J.; Erbe, L. H.; Mingarelli, A. B.
1987
Oscillation for nonlinear second order dynamic equations on a time scale. Zbl 1061.34018
Bohner, Martin; Erbe, Lynn; Peterson, Allan
2005
Kamenev type theorems for second order matrix differential systems. Zbl 0777.34024
Erbe, Lynn H.; Kong, Qingkai; Ruan, Shigui
1993
Riccati techniques and discrete oscillations. Zbl 0686.39001
Chen, Shaozhu; Erbe, Lynn H.
1989
Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. Zbl 1075.39010
Erbe, L.; Peterson, A.; Saker, S. H.
2005
Three-species food-chain models with mutual interference and time delays. Zbl 0592.92024
Erbe, L. H.; Freedman, H. I.; Sree Hari Rao, V.
1986
Oscillation criteria for second order linear equations on a time scale. Zbl 1050.39024
Erbe, L.
2001
Oscillation for first order linear differential equations with deviating arguments. Zbl 0723.34055
Erbe, L. H.; Zhang, B. G.
1988
Hille and Nehari type criteria for third-order dynamic equations. Zbl 1128.39009
Erbe, L.; Peterson, A.; Saker, S. H.
2007
Disconjugacy for linear Hamiltonian difference systems. Zbl 0762.39003
Erbe, Lynn H.; Yan, Pengxiang
1992
$$S^ 1$$-degree and global Hopf bifurcation theory of functional differential equations. Zbl 0765.34023
Erbe, L. H.; Krawcewicz, W.; Gȩba, K.; Wu, J.
1992
Oscillation criteria for nonlinear damped dynamic equations on time scales. Zbl 1162.39005
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2008
Boundedness and oscillation for nonlinear dynamic equations on a time scale. Zbl 1055.39007
Erbe, Lynn; Peterson, Allan
2004
Comparison theorems for linear dynamic equations on time scales. Zbl 1034.34042
Erbe, Lynn; Peterson, Allan; Řehák, Pavel
2002
Oscillation criteria for second order nonlinear delay equations. Zbl 0272.34095
Erbe, Lynn
1973
Two monotonicity results for nabla and delta fractional differences. Zbl 1327.39011
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Eigenvalue criteria for existence of positive solutions to nonlinear boundary value problems. Zbl 0970.34019
Erbe, L.
2000
Oscillation criteria for second-order matrix dynamic equations on a time scale. Zbl 1017.34030
Erbe, Lynn; Peterson, Allan
2002
Convexity for nabla and delta fractional differences. Zbl 1320.39003
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2015
Uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball. Zbl 0884.34025
Erbe, Lynn; Tang, Moxun
1997
Boundary value problems for singular second-order functional differential equations. Zbl 0816.34046
Erbe, L. H.; Kong, Qingkai
1994
Existence of solutions to boundary value problems for second order differential equations. Zbl 0517.34018
Erbe, L. H.
1982
Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. Zbl 1193.34135
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2009
Oscillation and nonoscillation for systems of self-adjoint second-order difference equations. Zbl 0687.39001
Chen, Shaozhu; Erbe, Lynn H.
1989
Existence results for boundary value problems of second order impulsive differential equations. Zbl 0711.34027
Erbe, Lynn H.; Liu, Xinzhi
1990
Eigenvalue conditions and positive solutions. Zbl 0949.34015
Erbe, Lynn; Peterson, Allan
2000
Positive solutions for singular nonlinear boundary value problems. Zbl 1007.34020
Erbe, Lynn H.; Mathsen, Ronald M.
2001
Oscillation criteria for half-linear delay dynamic equations on time scales. Zbl 1173.34037
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2009
Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. Zbl 1145.34329
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Multiplicity of positive solutions for higher order Sturm-Liouville problems. Zbl 0989.34012
Davis, John M.; Erbe, Lynn H.; Henderson, Johnny
2001
Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions. Zbl 1422.39027
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan
2016
Nabla dynamic equations on time scales. Zbl 1032.39007
Anderson, Douglas; Bullock, John; Erbe, Lynn; Peterson, Allan; Tran, Hoainam
2003
Nonlinear boundary value problems for differential inclusions $$y''\in F(t,y,y')$$. Zbl 0731.34078
Erbe, L. H.; Krawcewicz, W.
1991
Oscillation of third order nonlinear functional dynamic equations on time scales. Zbl 1213.34116
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
Existence and multiplicity of positive solutions to nonlinear boundary value problems. Zbl 0868.35035
Erbe, Lynn H.; Tang, M.
1996
Nonlinear boundary value problems for second order differential equations. Zbl 0284.34017
Erbe, Lynn H.
1970
Oscillation of second order linear difference equations. Zbl 0692.39001
Erbe, L. H.; Zhang, B. G.
1988
Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equations. Zbl 0339.34030
Erbe, L.
1976
Oscillation, nonoscillation, and asymptotic behavior for third order nonlinear differential equations. Zbl 0345.34023
Erbe, L.
1976
Structure of positive radial solutions of semilinear elliptic equations. Zbl 0871.34023
Erbe, Lynn; Tang, Moxun
1997
Oscillation results for second order differential systems. Zbl 0583.34027
Butler, G. J.; Erbe, L. H.
1986
Existence of solutions to boundary value problems for impulsive second order differential inclusions. Zbl 0784.34012
Erbe, L.; Krawcewicz, W.
1992
Monotonicity results for delta fractional differences revisited. Zbl 06760211
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan
2017
Monotonicity and convexity for nabla fractional $$(q,h)$$-differences. Zbl 1364.39009
Du, Feifei; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2016
Oscillation results for selfadjoint differential systems. Zbl 0588.34025
Butler, G. J.; Erbe, L. H.
1986
Oscillation results for second-order linear equations on a time scale. Zbl 1021.34012
Erbe, L.
2002
Kamenev-type oscillation criteria for second-order linear delay dynamic equations. Zbl 1104.34026
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Qualitative properties of Hamiltonian difference systems. Zbl 0768.39001
Erbe, Lynn H.; Yan, Pengxiang
1992
Riccati equations on a measure chain. Zbl 1008.34006
Erbe, Lynn; Peterson, Allan
2001
Existence and nonexistence of positive solutions for elliptic equations in an annulus. Zbl 0900.35144
Erbe, L. H.; Wang, Haiyan
1994
A composite coincidence degree with applications to boundary value problems of neutral equations. Zbl 0770.34053
Erbe, L. H.; Krawcewicz, W.; Wu, J. H.
1993
Existence, multiplicity and nonexistence of positive solutions to a differential equation on a measure chain. Zbl 0937.34025
Erbe, Lynn; Peterson, Allan; Mathsen, Ronald
2000
Some relations between the Caputo fractional difference operators and integer-order differences. Zbl 1321.39024
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Oscillation theorems for second order nonlinear differential equations. Zbl 0194.12102
Erbe, L.
1970
Weighted averaging techniques in oscillation theory for second order difference equations. Zbl 0762.39002
Erbe, Lynn H.; Yan, Pengxiang
1992
Quasi-solutions of nonlinear impulsive equations in abstract cones. Zbl 0662.34015
Erbe, L. H.; Liu, Xinzhi
1989
Oscillation results for second order scalar and matrix difference equations. Zbl 0807.39003
Chen, S.-Z.; Erbe, L.
1994
On the asymptotic behavior of solutions of Emden-Fowler equations on time scales. Zbl 1259.34093
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2012
Spectral parameter power series for Sturm-Liouville equations on time scales. Zbl 1245.34088
Erbe, Lynn; Mert, Raziye; Peterson, Allan
2012
Oscillation of third order functional dynamic equations with mixed arguments on time scales. Zbl 1213.34115
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
Oscillation theorems for second order linear differential equations. Zbl 0185.15903
Erbe, L.
1970
Bounded and zero-convergent solutions of a class of Stieltjes integro- differential equations. Zbl 0739.45005
Chen, Shaozhu; Huang, Qingguang; Erbe, L. H.
1991
Modeling persistence and mutual interference among subpopulations of ecological communities. Zbl 0571.92026
Erbe, L. H.; Freedman, H. I.
1985
Oscillation of even order nonlinear delay dynamic equations on time scales. Zbl 1274.34262
Erbe, Lynn; Mert, Raziye; Peterson, Allan; Zafer, Ağacık
2013
Oscillation results for a dynamic equation on a time scale. Zbl 1002.39024
Akin, Elvan; Erbe, Lynn; Peterson, Allan; Kaymakçalan, Billur
2001
Oscillation of solution to second-order half-linear delay dynamic equations on time scales. Zbl 1345.34150
Wu, Hongwu; Erbe, Lynn; Peterson, Allan
2016
Monotonicity and convexity for nabla fractional $$q$$-differences. Zbl 1362.39020
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2016
Hille-Kneser-type criteria for second-order dynamic equations on time scales. Zbl 1229.34136
Erbe, Lynn; Peterson, Allan C.; Saker, Samir H.
2006
Kiguradze-type oscillation theorems for second order superlinear dynamic equations on time scales. Zbl 1246.34066
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2011
Uniqueness of positive radial solutions of $$\Delta u+f(| x| ,u)=0$$. Zbl 1131.35334
Erbe, Lynn; Tang, Moxun
1998
Belohorec-type oscillation theorem for second order sublinear dynamic equations on time scales. Zbl 1229.34135
Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2011
Boundary value problems for ordinary differential equations. Zbl 0242.34022
Erbe, Lynn
1971
Oscillation of second order superlinear dynamic equations with damping on time scales. Zbl 1189.34133
Hassan, Taher S.; Erbe, Lynn; Peterson, Allan
2010
On the discrete Riccati equation and its applications to discrete Hamiltonian systems. Zbl 0836.39003
Erbe, Lynn H.; Yan, Pengxiang
1995
Comparison theorems and asymptotic behavior of solutions of discrete fractional equations. Zbl 1349.39006
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
On radial solutions of some semilinear elliptic equations. Zbl 0721.35020
Erbe, Lynn; Schmitt, Klaus
1988
Solvability of two-point boundary value problems for systems of nonlinear differential equations of the form $$y''=g(t,y,y',y'')$$. Zbl 0728.34004
Erbe, L. H.; Krawcewicz, W.; Kaczynski, T.
1990
Leray-Schauder degree for semilinear Fredholm maps and periodic boundary value problems of neutral equations. Zbl 0729.47058
Erbe, L. H.; Krawcewicz, W.; Wu, J.
1990
Oscillation of $$n$$th order superlinear dynamic equations on time scales. Zbl 1216.34100
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2011
Boundary value problems for second-order differential systems. Zbl 0635.34017
Erbe, L. H.; Palamides, P. K.
1987
Oscillation criteria for a forced second-order nonlinear dynamic equation. Zbl 1168.34025
Erbe, L.; Peterson, A.; Saker, S. H.
2008
Existence of solutions to second-order BVPs on time scales. Zbl 1088.39014
Erbe, Lynn; Peterson, Allan; Tisdell, Christopher C.
2005
On the existence of oscillatory solutions to nonlinear differential equations. Zbl 0345.34022
Erbe, Lynn H.; Muldowney, James S.
1976
Homoclinic solutions of discrete nonlinear systems via variational method. Zbl 1462.39003
Erbe, Lynn; Jia, Baoguo; Zhang, Qinqin
2019
Uniqueness of positive radial solutions of $$\Delta u+K(| x|)\gamma(u)=0$$. Zbl 1131.35333
Erbe, Lynn; Tang, Moxun
1998
Oscillation criteria for Hamiltonian matrix difference systems. Zbl 0794.39006
Erbe, L. H.; Yan, Pengxiang
1993
Periodic boundary value problems for second order integrodifferential equations of mixed type. Zbl 0799.45007
Erbe, L. H.; Guo, Dajun
1992
Oscillation criteria for matrix differential inequalities. Zbl 0275.34034
Allegretto, W.; Erbe, L.
1973
Oscillation criteria for second order nonlinear differential equations. Zbl 0296.34026
Erbe, L.
1972
Homoclinic solutions of discrete nonlinear systems via variational method. Zbl 1462.39003
Erbe, Lynn; Jia, Baoguo; Zhang, Qinqin
2019
Asymptotic behavior of solutions of fractional nabla $$q$$-difference equations. Zbl 1414.39003
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2019
Gronwall’s inequality for a nabla fractional difference system with a retarded argument and an application. Zbl 1429.39004
Chen, Churong; Mert, Raziye; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2019
A generalized $$h$$-fractional Gronwall’s inequality and its applications for nonlinear $$h$$-fractional difference systems with ‘maxima’. Zbl 1421.39002
Liu, Xiang; Peterson, Allan; Jia, Baoguo; Erbe, Lynn
2019
Stability analysis for a class of nabla $$(q,h)$$-fractional difference equations. Zbl 1410.39030
Liu, Xiang; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2019
Existence and uniqueness theorem of the solution to a class of nonlinear nabla fractional difference system with a time delay. Zbl 1403.39003
Chen, Churong; Jia, Baoguo; Liu, Xiang; Erbe, Lynn
2018
Two asymptotic results of solutions for nabla fractional $$(q,h)$$-difference equations. Zbl 1424.39047
Du, Feifei; Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2018
Asymptotic behavior of nabla half order $$h$$-difference equations. Zbl 1457.39005
Jia, Baoguo; Du, Feifei; Erbe, Lynn; Peterson, Allan
2018
Monotonicity results for delta fractional differences revisited. Zbl 06760211
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan
2017
The relation between nabla fractional differences and nabla integer differences. Zbl 07389825
Baoguo, Jia; Erbe, Lynn; Goodrich, Christopher; Peterson, Allan
2017
Liapunov functional and stability of linear nabla $$(q,h)$$-fractional difference equations. Zbl 1406.39021
Jia, Baoguo; Chen, Siyuan; Erbe, Lynn; Peterson, Allan
2017
Existence and rapid convergence results for nonlinear Caputo nabla fractional difference equations. Zbl 1413.39009
Liu, Xiang; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2017
Oscillation criteria for second order superlinear dynamic equations with oscillating coefficients. Zbl 1373.34134
Wu, Hongwu; Jia, Baoguo; Erbe, Lynn
2017
Survey of the qualitative properties of fractional difference operators: monotonicity, convexity, and asymptotic behavior of solutions. Zbl 1422.39027
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan
2016
Monotonicity and convexity for nabla fractional $$(q,h)$$-differences. Zbl 1364.39009
Du, Feifei; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2016
Oscillation of solution to second-order half-linear delay dynamic equations on time scales. Zbl 1345.34150
Wu, Hongwu; Erbe, Lynn; Peterson, Allan
2016
Monotonicity and convexity for nabla fractional $$q$$-differences. Zbl 1362.39020
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2016
Oscillation criteria for second order sublinear dynamic equations with oscillating coefficients. Zbl 1347.34140
Wu, Hongwu; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2016
Two monotonicity results for nabla and delta fractional differences. Zbl 1327.39011
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Convexity for nabla and delta fractional differences. Zbl 1320.39003
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2015
Some relations between the Caputo fractional difference operators and integer-order differences. Zbl 1321.39024
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Comparison theorems and asymptotic behavior of solutions of discrete fractional equations. Zbl 1349.39006
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Upper bounds for the distances between consecutive zeros of solutions of first order delay differential equations. Zbl 1320.34099
Wu, Hongwu; Erbe, Lynn; Peterson, Allan
2015
Theorems of Kiguradze-type and Belohorec-type revisited on time scales. Zbl 1318.34123
Wu, Hongwu; Jia, Baoguo; Erbe, Lynn
2015
An extended Halanay inequality of integral type on time scales. Zbl 1349.34397
Ou, Boqun; Jia, Baoguo; Erbe, Lynn
2015
A generalized Halanay-type inequality on time scales. Zbl 1335.34146
Ou, Boqun; Jia, Baoguo; Erbe, Lynn
2015
A Wong-type necessary and sufficient condition for nonoscillation of second order linear dynamic equations on time scales. Zbl 1343.34208
Erbe, Lynn; Mert, Raziye
2014
A Butler-type oscillation theorem for second-order dynamic equations on discrete timescales. Zbl 1304.34160
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2014
A Halanay-type inequality on time scales in higher dimensional spaces. Zbl 1301.34114
Jia, Baoguo; Erbe, Lynn; Mert, Raziye
2014
Oscillation of even order nonlinear delay dynamic equations on time scales. Zbl 1274.34262
Erbe, Lynn; Mert, Raziye; Peterson, Allan; Zafer, Ağacık
2013
An oscillation theorem for second order superlinear dynamic equations on time scales. Zbl 1297.34100
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2013
On the distance between consecutive zeros of solutions of first order delay differential equations. Zbl 1293.34083
Wu, Hong-Wu; Erbe, Lynn
2013
New oscillation criteria for second order sublinear dynamic equations. Zbl 1302.34135
Erbe, Lynn; Hassan, Taher S.
2013
On the asymptotic behavior of solutions of Emden-Fowler equations on time scales. Zbl 1259.34093
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2012
Spectral parameter power series for Sturm-Liouville equations on time scales. Zbl 1245.34088
Erbe, Lynn; Mert, Raziye; Peterson, Allan
2012
Oscillation theorems for second order sublinear dynamic equations on time scales. Zbl 1269.34073
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2012
Asymptotic behavior of $$n$$-th order dynamic equations. Zbl 1279.34106
Erbe, L.; Hovhannisyan, G.; Peterson, A.
2012
Kiguradze-type oscillation theorems for second order superlinear dynamic equations on time scales. Zbl 1246.34066
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2011
Belohorec-type oscillation theorem for second order sublinear dynamic equations on time scales. Zbl 1229.34135
Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2011
Oscillation of $$n$$th order superlinear dynamic equations on time scales. Zbl 1216.34100
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2011
Oscillation criteria for second order sublinear dynamic equations with damping term. Zbl 1228.34146
Hassan, Taher S.; Erbe, Lynn; Peterson, Allan
2011
Oscillation for a nonlinear dynamic system on time scales. Zbl 1232.34124
Erbe, Lynn; Mert, Raziye
2011
Asymptotic behavior of $$n$$-th order sublinear dynamic equations on time scales. Zbl 1235.34239
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2011
Oscillation of third order nonlinear functional dynamic equations on time scales. Zbl 1213.34116
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
Oscillation of third order functional dynamic equations with mixed arguments on time scales. Zbl 1213.34115
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
Oscillation of second order superlinear dynamic equations with damping on time scales. Zbl 1189.34133
Hassan, Taher S.; Erbe, Lynn; Peterson, Allan
2010
A Wong-type oscillation theorem for second order linear dynamic equations on time scales. Zbl 1193.34179
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2010
Interval oscillation criteria for forced second-order nonlinear delay dynamic equations with oscillatory potential. Zbl 1202.34162
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2010
Oscillation of sublinear Emden-Fowler dynamic equations on time scales. Zbl 1191.34107
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2010
Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. Zbl 1193.34135
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2009
Oscillation criteria for half-linear delay dynamic equations on time scales. Zbl 1173.34037
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2009
Nonoscillation for second order sublinear dynamic equations on time scales. Zbl 1187.34128
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2009
Oscillation and nonoscillation of solutions of second order linear dynamic equations with integrable coefficients on time scales. Zbl 1191.34109
Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2009
Oscillation of a family of $$q$$-difference equations. Zbl 1170.39002
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2009
Some new oscillation results for a nonlinear dynamic system on time scales. Zbl 1185.34141
Erbe, Lynn; Mert, Raziye
2009
Oscillation criteria for first order forced dynamic equations. Zbl 1299.34293
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2009
Oscillation criteria for nonlinear damped dynamic equations on time scales. Zbl 1162.39005
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2008
Oscillation criteria for a forced second-order nonlinear dynamic equation. Zbl 1168.34025
Erbe, L.; Peterson, A.; Saker, S. H.
2008
Basic existence, uniqueness and approximation results for positive solutions to nonlinear dynamic equations on time scales. Zbl 1158.34025
Erbe, L.; Peterson, A.; Tisdell, Christopher C.
2008
New comparison and oscillation theorems for second-order half-linear dynamic equations on time scales. Zbl 1165.34340
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2008
Oscillation criteria for second-order nonlinear delay dynamic equations. Zbl 1125.34046
Erbe, L.; Peterson, A.; Saker, S. H.
2007
Hille and Nehari type criteria for third-order dynamic equations. Zbl 1128.39009
Erbe, L.; Peterson, A.; Saker, S. H.
2007
On systems of boundary value problems for differential inclusions. Zbl 1126.34012
Erbe, Lynn; Tisdell, Christopher C.; Wong, Patricia J. Y.
2007
Recent results concerning dynamic equations on time scales. Zbl 1177.34008
Erbe, Lynn; Peterson, Allan
2007
Some new comparison results for second order linear dynamic equations. Zbl 1201.34142
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2007
Integral comparison theorems for second-order linear dynamic equations. Zbl 1127.39029
Erbe, Lynn; Peterson, Allan; Řehák, Pavel
2007
Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. Zbl 1145.34329
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Kamenev-type oscillation criteria for second-order linear delay dynamic equations. Zbl 1104.34026
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Hille-Kneser-type criteria for second-order dynamic equations on time scales. Zbl 1229.34136
Erbe, Lynn; Peterson, Allan C.; Saker, Samir H.
2006
On two point boundary value problems for second order differential inclusions. Zbl 1112.34008
Erbe, Lynn; Ma, Ruyun; Tisdell, Christopher C.
2006
A telescoping principle for oscillation of second order differential equations on a time scale. Zbl 1156.34021
Erbe, Lynn; Kong, Lingju; Kong, Qingkai
2006
Monotone solutions of dynamic systems on time scales. Zbl 1098.39010
Erbe, L.; Peterson, A.; Tisdell, C. C.
2006
Oscillation for nonlinear second order dynamic equations on a time scale. Zbl 1061.34018
Bohner, Martin; Erbe, Lynn; Peterson, Allan
2005
Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. Zbl 1075.39010
Erbe, L.; Peterson, A.; Saker, S. H.
2005
Existence of solutions to second-order BVPs on time scales. Zbl 1088.39014
Erbe, Lynn; Peterson, Allan; Tisdell, Christopher C.
2005
Square integrability of Gaussian bells on time scales. Zbl 1088.81058
Erbe, L.; Peterson, A.; Simon, M.
2005
Comparison theorems of Hille-Wintner type for dynamic equations on time scales. Zbl 1078.39015
Erbe, Lynn; Peterson, Allan
2005
Boundedness and oscillation for nonlinear dynamic equations on a time scale. Zbl 1055.39007
Erbe, Lynn; Peterson, Allan
2004
Some recent results in linear and nonlinear oscillation. Zbl 1073.34033
Erbe, Lynn; Peterson, Allan
2004
Oscillation criteria for second-order nonlinear dynamic equations on time scales. Zbl 1050.34042
Erbe, Lynn; Peterson, Allan; Saker, S. H.
2003
Nabla dynamic equations on time scales. Zbl 1032.39007
Anderson, Douglas; Bullock, John; Erbe, Lynn; Peterson, Allan; Tran, Hoainam
2003
An oscillation result for a nonlinear dynamic equation on a time scale. Zbl 1086.39004
Erbe, Lynn; Peterson, Allan
2003
Comparison theorems for linear dynamic equations on time scales. Zbl 1034.34042
Erbe, Lynn; Peterson, Allan; Řehák, Pavel
2002
Oscillation criteria for second-order matrix dynamic equations on a time scale. Zbl 1017.34030
Erbe, Lynn; Peterson, Allan
2002
Oscillation results for second-order linear equations on a time scale. Zbl 1021.34012
Erbe, L.
2002
Averaging techniques for self-adjoint matrix equations on a measure chain. Zbl 1014.39005
Erbe, Lynn; Peterson, Allan
2002
Existence of bounded solutions for second order dynamic equations. Zbl 1005.39018
Akin, Elvan; Bohner, Martin; Erbe, Lynn; Peterson, Allan
2002
Positive and monotone solutions of a boundary value problem for second order singular ordinary differential equations. Zbl 1231.34037
Erbe, L. H.; Palamides, P. K.
2002
Oscillation criteria for second order linear equations on a time scale. Zbl 1050.39024
Erbe, L.
2001
Positive solutions for singular nonlinear boundary value problems. Zbl 1007.34020
Erbe, Lynn H.; Mathsen, Ronald M.
2001
Multiplicity of positive solutions for higher order Sturm-Liouville problems. Zbl 0989.34012
Davis, John M.; Erbe, Lynn H.; Henderson, Johnny
2001
Riccati equations on a measure chain. Zbl 1008.34006
Erbe, Lynn; Peterson, Allan
2001
Oscillation results for a dynamic equation on a time scale. Zbl 1002.39024
Akin, Elvan; Erbe, Lynn; Peterson, Allan; Kaymakçalan, Billur
2001
Factoring linear differential operators on measure chains. Zbl 1001.34029
Erbe, Lynn H.; Mathsen, Ronald M.; Peterson, Allan
2001
Positive solutions for a nonlinear differential equation on a measure chain. Zbl 0963.34020
Erbe, L.; Peterson, A.
2000
Eigenvalue criteria for existence of positive solutions to nonlinear boundary value problems. Zbl 0970.34019
Erbe, L.
2000
Eigenvalue conditions and positive solutions. Zbl 0949.34015
Erbe, Lynn; Peterson, Allan
2000
Existence, multiplicity and nonexistence of positive solutions to a differential equation on a measure chain. Zbl 0937.34025
Erbe, Lynn; Peterson, Allan; Mathsen, Ronald
2000
Green’s functions and comparison theorems for differential equations on measure chains. Zbl 0938.34027
Erbe, Lynn; Peterson, Allan
1999
Uniqueness of positive radial solutions of $$\Delta u+f(| x| ,u)=0$$. Zbl 1131.35334
Erbe, Lynn; Tang, Moxun
1998
...and 109 more Documents
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### Cited by 1,657 Authors

 105 Agarwal, Ravi P. 89 Erbe, Lynn Harry 60 O’Regan, Donal 52 Peterson, Allan C. 49 Li, Tongxing 48 Wong, Patricia J. Y. 42 Bohner, Martin J. 40 Saker, Samir H. 36 Henderson, Johnny Lee 35 Grace, Said Rezk 33 Ge, Weigao 30 Goodrich, Christopher S. 29 Chatzarakis, George E. 29 Graef, John R. 29 Meng, Fanwei 29 Wang, Qiru 27 Džurina, Jozef 27 Ma, Ruyun 26 Jia, Baoguo 25 Han, Zhenlai 25 Zhang, Binggen 24 Kong, Qingkai 23 Tang, Xianhua 22 Anderson, Douglas Robert 22 Hassan, Taher S. 22 Zhang, Chenghui 21 Yu, Jian-She 19 Liu, Xinzhi 19 Stavroulakis, Ioannis P. 19 Sun, Shurong 18 Li, Wan-Tong 18 Thandapani, Ethiraju 17 Baculíková, Blanka 17 Kong, Lingju 17 Liu, Lishan 16 Eloe, Paul W. 16 Wong, Fu-Hsiang 15 Benchohra, Mouffak 15 Karpuz, Başak 15 Sun, Yuangong 14 Braverman, Elena 14 Diblík, Josef 14 Ntouyas, Sotiris K. 14 Wu, Jianhong 13 Jadlovská, Irena 13 Krawcewicz, Wieslaw Z. 13 Li, Yongxiang 13 Shen, Jianhua 13 Šimon Hilscher, Roman 13 Wong, James S. W. 13 Zhou, Zhan 12 Liu, Yuji 12 Wang, Haiyan 11 Cabada, Alberto 11 Došlá, Zuzana 11 Jiang, Daqing 11 Liu, Haidong 11 Ocalan, Ozkan 11 Shi, Haiping 11 Sitthiwirattham, Thanin 11 Sun, Jianping 11 Wu, Yonghong 11 Zhou, Yong 10 Alzabut, Jehad O. 10 Bainov, Drumi Dimitrov 10 Baoguo, Jia 10 Berezansky, Leonid M. 10 Došlý, Ondřej 10 Feng, Qinghua 10 Li, Weinian 10 Marini, Mauro 10 Parhi, Narahari 10 Prasad, Kapula Rajendra 10 Řehák, Pavel 10 Sun, Taixiang 10 Thompson, Harold Bevan 10 Tisdell, Christopher C. 10 Wu, Hongwu 10 Zhang, Quanxin 10 Zheng, Zhaowen 9 Cecchi, Mariella 9 El-Morshedy, Hassan A. 9 Feng, Meiqiang 9 Lalli, Bikkar S. 9 Li, Yongkun 9 Merdivenci Atici, Ferhan 9 Papageorgiou, Nikolaos S. 9 Sun, Jingxian 9 Tiryaki, Aydin 9 Yan, Jurang 9 Yang, Qigui 9 Zafer, Ağacık 8 Freedman, Herbert Irving 8 Han, Maoan 8 Kamont, Zdzisław 8 Li, Fuyi 8 Li, Yong 8 Liu, Xia 8 Lizama, Carlos 8 Minchev, Emil ...and 1,557 more Authors
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### Cited in 236 Serials

 237 Journal of Mathematical Analysis and Applications 155 Computers & Mathematics with Applications 138 Applied Mathematics and Computation 127 Advances in Difference Equations 122 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 81 Applied Mathematics Letters 67 Journal of Difference Equations and Applications 66 Abstract and Applied Analysis 63 Journal of Computational and Applied Mathematics 61 Rocky Mountain Journal of Mathematics 56 Journal of Differential Equations 50 Mathematical and Computer Modelling 45 Journal of Applied Mathematics and Computing 39 Nonlinear Analysis. Theory, Methods & Applications 36 Proceedings of the American Mathematical Society 33 Discrete Dynamics in Nature and Society 27 Boundary Value Problems 26 Applicable Analysis 25 Czechoslovak Mathematical Journal 20 Mathematica Slovaca 18 Applied Mathematics. Series B (English Edition) 18 Journal of Inequalities and Applications 18 Nonlinear Analysis. Real World Applications 15 Annali di Matematica Pura ed Applicata. Serie Quarta 15 Acta Mathematicae Applicatae Sinica. English Series 14 International Journal of Differential Equations 13 Mathematische Nachrichten 13 Differential Equations and Dynamical Systems 12 Journal of Applied Mathematics 12 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 12 Journal of Fixed Point Theory and Applications 11 Opuscula Mathematica 11 Mediterranean Journal of Mathematics 10 Applied Mathematics and Mechanics. (English Edition) 9 Mathematical Methods in the Applied Sciences 9 Chaos, Solitons and Fractals 9 Filomat 9 Acta Mathematica Sinica. English Series 8 Mathematical Biosciences 8 Results in Mathematics 8 Communications in Nonlinear Science and Numerical Simulation 8 Hacettepe Journal of Mathematics and Statistics 7 Bulletin of the Australian Mathematical Society 7 Transactions of the American Mathematical Society 7 Acta Applicandae Mathematicae 7 Linear Algebra and its Applications 7 Georgian Mathematical Journal 7 Fractional Calculus & Applied Analysis 7 The ANZIAM Journal 7 Science China. Mathematics 7 Electronic Journal of Mathematical Analysis and Applications EJMAA 7 Journal of Function Spaces 6 Journal of Mathematical Physics 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Russian Mathematics 6 Turkish Journal of Mathematics 6 Nonlinear Dynamics 6 Central European Journal of Mathematics 6 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 6 Journal of Applied Analysis and Computation 6 AIMS Mathematics 5 Archiv der Mathematik 5 International Journal of Mathematics and Mathematical Sciences 5 Tohoku Mathematical Journal. Second Series 5 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 5 Journal of Integral Equations and Applications 5 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Positivity 5 Analysis (München) 5 Qualitative Theory of Dynamical Systems 4 Zeitschrift für Analysis und ihre Anwendungen 4 Acta Mathematica Hungarica 4 Physica D 4 Journal of Mathematical Sciences (New York) 4 Electronic Journal of Differential Equations (EJDE) 4 Complexity 4 Discrete and Continuous Dynamical Systems 4 Functional Differential Equations 4 Advanced Nonlinear Studies 4 Nonlinear Oscillations 4 Discrete and Continuous Dynamical Systems. Series S 3 Indian Journal of Pure & Applied Mathematics 3 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 3 Journal of Functional Analysis 3 Journal of Optimization Theory and Applications 3 Mathematics and Computers in Simulation 3 Monatshefte für Mathematik 3 Numerical Functional Analysis and Optimization 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Acta Mathematica Sinica. New Series 3 Tatra Mountains Mathematical Publications 3 Fractals 3 Arab Journal of Mathematical Sciences 3 Mathematical Problems in Engineering 3 Journal of Dynamical and Control Systems 3 Mathematical Modelling and Analysis 3 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 3 Discrete and Continuous Dynamical Systems. Series B 3 Communications on Pure and Applied Analysis ...and 136 more Serials
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### Cited in 45 Fields

 1,576 Ordinary differential equations (34-XX) 596 Difference and functional equations (39-XX) 249 Operator theory (47-XX) 194 Partial differential equations (35-XX) 154 Real functions (26-XX) 133 Biology and other natural sciences (92-XX) 72 Dynamical systems and ergodic theory (37-XX) 68 Integral equations (45-XX) 54 Numerical analysis (65-XX) 48 Systems theory; control (93-XX) 24 Calculus of variations and optimal control; optimization (49-XX) 24 Global analysis, analysis on manifolds (58-XX) 8 Mechanics of particles and systems (70-XX) 7 Special functions (33-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 6 Measure and integration (28-XX) 6 Integral transforms, operational calculus (44-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Functions of a complex variable (30-XX) 4 Functional analysis (46-XX) 4 Quantum theory (81-XX) 3 Approximations and expansions (41-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Abstract harmonic analysis (43-XX) 3 General topology (54-XX) 3 Probability theory and stochastic processes (60-XX) 3 Fluid mechanics (76-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Sequences, series, summability (40-XX) 2 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 2 Optics, electromagnetic theory (78-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Potential theory (31-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)