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## Erbe, Lynn Harry

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 Author ID: erbe.lynn-h Published as: Erbe, L.; Erbe, L. H.; Erbe, Lynn; Erbe, Lynn H. External Links: MGP
 Documents Indexed: 257 Publications since 1969, including 4 Books Reviewing Activity: 2 Reviews Biographic References: 1 Publication
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#### Co-Authors

 37 single-authored 71 Peterson, Allan C. 29 Jia, Baoguo 14 Baoguo, Jia 14 Krawcewicz, Wieslaw Z. 13 Peterson, Alan 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 Tang, Moxun 6 Wu, Hongwu 5 Chen, Shaozhu 5 Guo, Dajun 5 Liu, Xiang 5 Tisdell, Christopher C. 5 Yan, Pengxiang 4 Du, Feifei 4 Mathsen, Ronald M. 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 Goodrich, Christopher S. 2 Knobloch, Hans-Wilhelm 2 Muldowney, James S. 2 Mysore, S. 2 Oganesyan, Gro R. 2 Ou, Boqun 2 Řehák, Pavel 2 Wen, Lizhi 2 Xia, Huaxing 2 Xu, Zhiting 2 Yu, Jian-She 1 Allegretto, Walter 1 Anderson, Douglas Robert 1 Bullock, John 1 Chen, Siyuan 1 Davis, John M. 1 Gensler, Scott 1 Henderson, Johnny Lee 1 Hilger, Stefan 1 Hu, Wei 1 Huang, Qingguang 1 Kaczynski, Tomasz 1 Kaymakçalan, Billur 1 Kong, Lingju 1 Lee, Sung-Joon 1 Li, Longtu 1 Lu, Hong 1 Ma, Ruyun 1 Mingarelli, Angelo B. 1 Peschke, Georg 1 Ruan, Shigui 1 Seshagiri Rao, K. V. V. 1 Simon, Marvin K. 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 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) 16 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

205 Publications have been cited 3,562 times in 2,221 Documents Cited by Year
Oscillation theory for functional differential equations. Zbl 0821.34067
Erbe, L. H.; Kong, Qingkai; Zhang, B. G.
1994
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
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
Sturmian theory on measure chains. Zbl 0868.39007
Erbe, Lynn; Hilger, Stefan
1993
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
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
Kamenev type theorems for second order matrix differential systems. Zbl 0777.34024
Erbe, Lynn H.; Kong, Qingkai; Ruan, Shigui
1993
Oscillation for nonlinear second order dynamic equations on a time scale. Zbl 1061.34018
Bohner, Martin; Erbe, Lynn; Peterson, Allan
2005
Oscillation criteria for second order linear equations on a time scale. Zbl 1050.39024
Erbe, L.
2001
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
Disconjugacy for linear Hamiltonian difference systems. Zbl 0762.39003
Erbe, Lynn H.; Yan, Pengxiang
1992
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
Hille and Nehari type criteria for third-order dynamic equations. Zbl 1128.39009
Erbe, L.; Peterson, A.; Saker, S. H.
2007
Oscillation criteria for nonlinear damped dynamic equations on time scales. Zbl 1162.39005
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2008
Oscillation for first order linear differential equations with deviating arguments. Zbl 0723.34055
Erbe, L. H.; Zhang, B. G.
1988
Boundedness and oscillation for nonlinear dynamic equations on a time scale. Zbl 1055.39007
Erbe, Lynn; Peterson, Allan
2004
$$S^ 1$$-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 second order nonlinear delay equations. Zbl 0272.34095
Erbe, Lynn
1973
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
Boundary value problems for singular second-order functional differential equations. Zbl 0816.34046
Erbe, L. H.; Kong, Qingkai
1994
Uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball. Zbl 0884.34025
Erbe, Lynn; Tang, Moxun
1997
Eigenvalue criteria for existence of positive solutions to nonlinear boundary value problems. Zbl 0970.34019
Erbe, L.
2000
Existence of solutions to boundary value problems for second order differential equations. Zbl 0517.34018
Erbe, L. H.
1982
Existence results for boundary value problems of second order impulsive differential equations. Zbl 0711.34027
Erbe, Lynn H.; Liu, Xinzhi
1990
Oscillation and nonoscillation for systems of self-adjoint second-order difference equations. Zbl 0687.39001
Chen, Shaozhu; Erbe, Lynn H.
1989
Positive solutions for singular nonlinear boundary value problems. Zbl 1007.34020
Erbe, Lynn H.; Mathsen, Ronald M.
2001
Oscillation criteria for nonlinear functional neutral dynamic equations on time scales. Zbl 1193.34135
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2009
Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. Zbl 1145.34329
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Eigenvalue conditions and positive solutions. Zbl 0949.34015
Erbe, Lynn; Peterson, Allan
2000
Nonlinear boundary value problems for differential inclusions $$y''\in F(t,y,y')$$. Zbl 0731.34078
Erbe, L. H.; Krawcewicz, W.
1991
Multiplicity of positive solutions for higher order Sturm-Liouville problems. Zbl 0989.34012
Davis, John M.; Erbe, Lynn H.; Henderson, Johnny
2001
Existence and multiplicity of positive solutions to nonlinear boundary value problems. Zbl 0868.35035
Erbe, Lynn H.; Tang, M.
1996
Oscillation of third order nonlinear functional dynamic equations on time scales. Zbl 1213.34116
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
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 of second order linear difference equations. Zbl 0692.39001
Erbe, L. H.; Zhang, B. G.
1988
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
Nabla dynamic equations on time scales. Zbl 1032.39007
Anderson, Douglas; Bullock, John; Erbe, Lynn; Peterson, Allan; Tran, Hoainam
2003
Existence of oscillatory solutions and asymptotic behavior for a class of third order linear differential equations. Zbl 0339.34030
Erbe, L.
1976
Nonlinear boundary value problems for second order differential equations. Zbl 0284.34017
Erbe, Lynn H.
1970
Structure of positive radial solutions of semilinear elliptic equations. Zbl 0871.34023
Erbe, Lynn; Tang, Moxun
1997
Oscillation, nonoscillation, and asymptotic behavior for third order nonlinear differential equations. Zbl 0345.34023
Erbe, L.
1976
Existence of solutions to boundary value problems for impulsive second order differential inclusions. Zbl 0784.34012
Erbe, L.; Krawcewicz, W.
1992
Oscillation results for second order differential systems. Zbl 0583.34027
Butler, G. J.; Erbe, L. H.
1986
Oscillation results for second-order linear equations on a time scale. Zbl 1021.34012
Erbe, L.
2002
Qualitative properties of Hamiltonian difference systems. Zbl 0768.39001
Erbe, Lynn H.; Yan, Pengxiang
1992
Oscillation results for selfadjoint differential systems. Zbl 0588.34025
Butler, G. J.; Erbe, L. H.
1986
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
Kamenev-type oscillation criteria for second-order linear delay dynamic equations. Zbl 1104.34026
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Riccati equations on a measure chain. Zbl 1008.34006
Erbe, Lynn; Peterson, Allan
2001
Monotonicity results for delta fractional differences revisited. Zbl 06760211
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; Peterson, Allan
2017
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
Existence and nonexistence of positive solutions for elliptic equations in an annulus. Zbl 0900.35144
Erbe, L. H.; Wang, Haiyan
1994
Monotonicity and convexity for nabla fractional $$(q,h)$$-differences. Zbl 1364.39009
Du, Feifei; Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2016
Weighted averaging techniques in oscillation theory for second order difference equations. Zbl 0762.39002
Erbe, Lynn H.; Yan, Pengxiang
1992
Oscillation theorems for second order nonlinear differential equations. Zbl 0194.12102
Erbe, L.
1970
Spectral parameter power series for Sturm-Liouville equations on time scales. Zbl 1245.34088
Erbe, Lynn; Mert, Raziye; Peterson, Allan
2012
Oscillation results for second order scalar and matrix difference equations. Zbl 0807.39003
Chen, S.-Z.; Erbe, L.
1994
Bounded and zero-convergent solutions of a class of Stieltjes integro- differential equations. Zbl 0739.45005
Chen, Shaozhu; Huang, Qingguang; Erbe, L. H.
1991
Quasi-solutions of nonlinear impulsive equations in abstract cones. Zbl 0662.34015
Erbe, L. H.; Liu, Xinzhi
1989
Oscillation theorems for second order linear differential equations. Zbl 0185.15903
Erbe, L.
1970
Some relations between the Caputo fractional difference operators and integer-order differences. Zbl 1321.39024
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Kiguradze-type oscillation theorems for second order superlinear dynamic equations on time scales. Zbl 1246.34066
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2011
Oscillation of third order functional dynamic equations with mixed arguments on time scales. Zbl 1213.34115
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan
2010
Hille-Kneser-type criteria for second-order dynamic equations on time scales. Zbl 1229.34136
Erbe, Lynn; Peterson, Allan C.; Saker, Samir H.
2006
Oscillation results for a dynamic equation on a time scale. Zbl 1002.39024
Akin, Elvan; Erbe, Lynn; Peterson, Allan; Kaymakçalan, Billur
2001
Modeling persistence and mutual interference among subpopulations of ecological communities. Zbl 0571.92026
Erbe, L. H.; Freedman, H. I.
1985
Oscillation criteria for second order nonlinear differential equations. Zbl 0296.34026
Erbe, L.
1972
Boundary value problems for ordinary differential equations. Zbl 0242.34022
Erbe, Lynn
1971
Comparison theorems and asymptotic behavior of solutions of discrete fractional equations. Zbl 1349.39006
Jia, Baoguo; Erbe, Lynn; Peterson, Allan
2015
Oscillation of even order nonlinear delay dynamic equations on time scales. Zbl 1274.34262
Erbe, Lynn; Mert, Raziye; Peterson, Allan; Zafer, Ağacık
2013
Oscillation of second order superlinear dynamic equations with damping on time scales. Zbl 1189.34133
Hassan, Taher S.; Erbe, Lynn; Peterson, Allan
2010
Uniqueness of positive radial solutions of $$\Delta u+f(| x| ,u)=0$$. Zbl 1131.35334
Erbe, Lynn; Tang, Moxun
1998
Oscillation of $$n$$th order superlinear dynamic equations on time scales. Zbl 1216.34100
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2011
On the discrete Riccati equation and its applications to discrete Hamiltonian systems. Zbl 0836.39003
Erbe, Lynn H.; Yan, Pengxiang
1995
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
On radial solutions of some semilinear elliptic equations. Zbl 0721.35020
Erbe, Lynn; Schmitt, Klaus
1988
On the asymptotic behavior of solutions of Emden-Fowler equations on time scales. Zbl 1259.34093
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2012
Belohorec-type oscillation theorem for second order sublinear dynamic equations on time scales. Zbl 1229.34135
Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2011
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
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
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
Boundary value problems for second-order differential systems. Zbl 0635.34017
Erbe, L. H.; Palamides, P. K.
1987
On the existence of oscillatory solutions to nonlinear differential equations. Zbl 0345.34022
Erbe, Lynn H.; Muldowney, James S.
1976
Oscillation criteria for matrix differential inequalities. Zbl 0275.34034
Allegretto, W.; Erbe, L.
1973
Monotonicity and convexity for nabla fractional $$q$$-differences. Zbl 1362.39020
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2016
A Wong-type oscillation theorem for second order linear dynamic equations on time scales. Zbl 1193.34179
Baoguo, Jia; Erbe, Lynn; Peterson, Allan
2010
Nonoscillation for second order sublinear dynamic equations on time scales. Zbl 1187.34128
Erbe, Lynn; Baoguo, Jia; Peterson, Allan
2009
Uniqueness of positive radial solutions of $$\Delta u+K(| x|)\gamma(u)=0$$. Zbl 1131.35333
Erbe, Lynn; Tang, Moxun
1998
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
Two asymptotic results of solutions for nabla fractional $$(q,h)$$-difference equations. Zbl 1424.39047
Du, Feifei; Erbe, Lynn; Jia, Baoguo; Peterson, Allan
2018
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
Monotonicity results for delta fractional differences revisited. Zbl 06760211
Erbe, Lynn; Goodrich, Christopher S.; Jia, Baoguo; 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
Monotonicity and convexity for nabla fractional $$q$$-differences. Zbl 1362.39020
Baoguo, Jia; 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
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 Halanay-type inequality on time scales in higher dimensional spaces. Zbl 1301.34114
Jia, Baoguo; 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
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
Spectral parameter power series for Sturm-Liouville equations on time scales. Zbl 1245.34088
Erbe, Lynn; Mert, Raziye; Peterson, Allan
2012
On the asymptotic behavior of solutions of Emden-Fowler equations on time scales. Zbl 1259.34093
Erbe, Lynn; Baoguo, Jia; 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
Oscillation of $$n$$th order superlinear dynamic equations on time scales. Zbl 1216.34100
Erbe, Lynn; Baoguo, Jia; 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 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
A telescoping principle for oscillation of second order differential equations on a time scale. Zbl 1156.34021
Erbe, Lynn; Kong, Lingju; Kong, Qingkai
2006
On two point boundary value problems for second order differential inclusions. Zbl 1112.34008
Erbe, Lynn; Ma, Ruyun; Tisdell, Christopher C.
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
Uniqueness of positive radial solutions of $$\Delta u+K(| x|)\gamma(u)=0$$. Zbl 1131.35333
Erbe, Lynn; Tang, Moxun
1998
Uniqueness theorems for positive radial solutions of quasilinear elliptic equations in a ball. Zbl 0884.34025
Erbe, Lynn; Tang, Moxun
1997
Structure of positive radial solutions of semilinear elliptic equations. Zbl 0871.34023
Erbe, Lynn; Tang, Moxun
1997
Existence and multiplicity of positive solutions to nonlinear boundary value problems. Zbl 0868.35035
Erbe, Lynn H.; Tang, M.
1996
Positive radial solutions to nonlinear boundary value problems for semilinear elliptic problems. Zbl 0845.35033
Erbe, L. H.; Tang, M.
1996
...and 105 more Documents
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#### Cited by 1,706 Authors

 109 Agarwal, Ravi P. 88 Erbe, Lynn Harry 60 O’Regan, Donal 49 Li, Tongxing 48 Wong, Patricia J. Y. 42 Bohner, Martin J. 40 Peterson, Allan C. 40 Saker, Samir H. 36 Henderson, Johnny Lee 34 Ge, Weigao 32 Meng, Fanwei 29 Džurina, Jozef 29 Tang, Xianhua 29 Zhang, Binggen 27 Grace, Said Rezk 27 Graef, John R. 27 Wang, Qiru 26 Jia, Baoguo 26 Ma, Ruyun 25 Kong, Qingkai 24 Zhang, Chenghui 23 Han, Zhenlai 23 Yan, Jurang 22 Anderson, Douglas Robert 22 Chatzarakis, George E. 22 Diblík, Josef 22 Goodrich, Christopher S. 22 Hassan, Taher S. 21 Braverman, Elena 21 Yu, Jian-She 20 Baculíková, Blanka 20 Li, Wan-Tong 20 Stavroulakis, Ioannis P. 19 Berezansky, Leonid M. 19 Liu, Xinzhi 18 Sun, Shurong 17 Benchohra, Mouffak 17 Kong, Lingju 17 Liu, Lishan 17 Zhou, Yong 16 Shen, Jianhua 16 Thandapani, Ethiraju 16 Wong, Fu-Hsiang 15 Eloe, Paul W. 15 Karpuz, Başak 15 Sun, Yuangong 14 Ntouyas, Sotiris K. 14 Wong, James S. W. 14 Wu, Jianhong 13 El-Morshedy, Hassan A. 13 Krawcewicz, Wieslaw Z. 13 Li, Weinian 13 Li, Yongxiang 13 Liu, Yuji 13 Ocalan, Ozkan 13 Šimon Hilscher, Roman 13 Zhang, Quanxin 12 Tisdell, Christopher C. 12 Wang, Haiyan 12 Wu, Yonghong 11 Cabada, Alberto 11 Došlá, Zuzana 11 Jiang, Daqing 11 Shi, Haiping 11 Sun, Jianping 11 Wang, Peiguang 11 Wu, Hongwu 11 Zafer, Ağacık 10 Bainov, Drumi Dimitrov 10 Došlý, Ondřej 10 Feng, Qinghua 10 Kang, Shin Min 10 Liu, Zeqing 10 Marini, Mauro 10 Parhi, Narahari 10 Philos, Christos G. 10 Prasad, Kapula Rajendra 10 Řehák, Pavel 10 Sun, Taixiang 10 Thompson, Harold Bevan 10 Zheng, Zhaowen 10 Zhou, Zhan 9 Baoguo, Jia 9 Cecchi, Mariella 9 Feng, Meiqiang 9 Lalli, Bikkar S. 9 Li, Yongkun 9 Minchev, Emil 9 Papageorgiou, Nikolaos S. 9 Peterson, Alan 9 Rogovchenko, Yuri V. 9 Sun, Jingxian 9 Tiryaki, Aydin 9 Xu, Zhiting 9 Yang, Qigui 9 Zhang, Zhenguo 8 Candan, Tuncay 8 Freedman, Herbert Irving 8 Han, Maoan 8 Jadlovská, Irena ...and 1,606 more Authors
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#### Cited in 215 Serials

 272 Journal of Mathematical Analysis and Applications 173 Computers & Mathematics with Applications 165 Applied Mathematics and Computation 137 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 111 Advances in Difference Equations 100 Applied Mathematics Letters 74 Journal of Computational and Applied Mathematics 66 Abstract and Applied Analysis 64 Journal of Difference Equations and Applications 60 Rocky Mountain Journal of Mathematics 57 Journal of Differential Equations 57 Mathematical and Computer Modelling 43 Journal of Applied Mathematics and Computing 41 Nonlinear Analysis. Theory, Methods & Applications 36 Proceedings of the American Mathematical Society 33 Discrete Dynamics in Nature and Society 25 Applicable Analysis 25 Czechoslovak Mathematical Journal 22 Boundary Value Problems 18 Nonlinear Analysis. Real World Applications 17 Mathematica Slovaca 16 Applied Mathematics. Series B (English Edition) 15 Annali di Matematica Pura ed Applicata. Serie Quarta 15 Acta Mathematicae Applicatae Sinica. English Series 14 Journal of Inequalities and Applications 14 International Journal of Differential Equations 13 Mathematische Nachrichten 13 Differential Equations and Dynamical Systems 12 Journal of Applied Mathematics 11 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 11 Mediterranean Journal of Mathematics 10 Applied Mathematics and Mechanics. (English Edition) 10 Opuscula Mathematica 10 Journal of Fixed Point Theory and Applications 9 Mathematical Methods in the Applied Sciences 9 Chaos, Solitons and Fractals 8 Mathematical Biosciences 8 Results in Mathematics 8 Acta Mathematica Sinica. English Series 8 Communications in Nonlinear Science and Numerical Simulation 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 The ANZIAM Journal 7 Science China. Mathematics 7 Electronic Journal of Mathematical Analysis and Applications EJMAA 6 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 6 Russian Mathematics 6 Turkish Journal of Mathematics 6 Nonlinear Dynamics 6 Fractional Calculus & Applied Analysis 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 Journal of Function Spaces 5 Journal of Mathematical Physics 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 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Positivity 4 Archiv der Mathematik 4 Zeitschrift für Analysis und ihre Anwendungen 4 Acta Mathematica Hungarica 4 Physica D 4 Journal of Integral Equations and Applications 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 Analysis (München) 4 Advanced Nonlinear Studies 4 Nonlinear Oscillations 3 Indian Journal of Pure & Applied Mathematics 3 Journal of the Franklin Institute 3 Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 3 Journal of Functional Analysis 3 Journal of Optimization Theory and Applications 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 Arab Journal of Mathematical Sciences 3 Mathematical Problems in Engineering 3 Journal of Dynamical and Control Systems 3 Qualitative Theory of Dynamical Systems 3 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 3 Communications on Pure and Applied Analysis 3 Analysis and Applications (Singapore) 3 Complex Variables and Elliptic Equations 3 Asian-European Journal of Mathematics 3 International Journal of Biomathematics 2 International Journal of Theoretical Physics 2 Journal of Mathematical Biology 2 Mathematical Notes 2 Mathematical Proceedings of the Cambridge Philosophical Society ...and 115 more Serials
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#### Cited in 44 Fields

 1,633 Ordinary differential equations (34-XX) 563 Difference and functional equations (39-XX) 244 Operator theory (47-XX) 191 Partial differential equations (35-XX) 130 Biology and other natural sciences (92-XX) 109 Real functions (26-XX) 70 Dynamical systems and ergodic theory (37-XX) 68 Integral equations (45-XX) 48 Numerical analysis (65-XX) 45 Systems theory; control (93-XX) 25 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) 6 Linear and multilinear algebra; matrix theory (15-XX) 5 Special functions (33-XX) 5 Integral transforms, operational calculus (44-XX) 5 Functional analysis (46-XX) 5 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 4 Measure and integration (28-XX) 4 Functions of a complex variable (30-XX) 4 Probability theory and stochastic processes (60-XX) 3 Approximations and expansions (41-XX) 3 Abstract harmonic analysis (43-XX) 3 General topology (54-XX) 3 Quantum theory (81-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Sequences, series, summability (40-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 2 Fluid mechanics (76-XX) 2 Optics, electromagnetic theory (78-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-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 Statistics (62-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)