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Erschienen in: Journal of Applied Mathematics and Computing 1-2/2016

01.02.2016 | Original Research

Multiple periodic solutions of functional differential equations with impulses on time scales

verfasst von: Zhijun Zeng

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2016

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Abstract

In this paper, sufficient criteria are established for the existence of periodic solutions of a class of functional dynamic equations with impulses on time scales. The systems under consideration are general enough to incorporate many mathematical models arising in ecological equations. The approach is mainly based on the Krasnoselskii fixed point theorem, which has been extensively applied to the study of existence problem.

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Literatur
1.
Zurück zum Zitat Bi, L., Bohner, M., Fan, M.: Periodic solutions of functional dynamic equations with infinite delay. Nonlinear Anal. 68, 1226–1245 (2008)MathSciNetCrossRefMATH Bi, L., Bohner, M., Fan, M.: Periodic solutions of functional dynamic equations with infinite delay. Nonlinear Anal. 68, 1226–1245 (2008)MathSciNetCrossRefMATH
2.
Zurück zum Zitat Bohner, M., Fan, M., Zhang, J.M.: Existence of periodic solutions in predator-prey and competition dynamic systems. Nonlinear Anal. 7, 1193–1204 (2006)MathSciNetCrossRefMATH Bohner, M., Fan, M., Zhang, J.M.: Existence of periodic solutions in predator-prey and competition dynamic systems. Nonlinear Anal. 7, 1193–1204 (2006)MathSciNetCrossRefMATH
3.
Zurück zum Zitat Li, W., Huo, H.F.: Existence and global attractivity of positive periodic solutions of functional differential with impulsives. Nonlinear Anal. 59, 857–877 (2004)MathSciNetCrossRefMATH Li, W., Huo, H.F.: Existence and global attractivity of positive periodic solutions of functional differential with impulsives. Nonlinear Anal. 59, 857–877 (2004)MathSciNetCrossRefMATH
4.
Zurück zum Zitat Li, X.Y., Lin, X.N., Jiang, D.Q., Zhang, X.Y.: Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects. Nonlinear Anal. 62, 683–701 (2005)MathSciNetCrossRefMATH Li, X.Y., Lin, X.N., Jiang, D.Q., Zhang, X.Y.: Existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects. Nonlinear Anal. 62, 683–701 (2005)MathSciNetCrossRefMATH
5.
Zurück zum Zitat Wan, A., Jiang, D., Xu, X.: A new existence theory for positive periodic solutions to functional differential equations. Comput. Math. Appl. 47, 1257–1262 (2004)MathSciNetCrossRefMATH Wan, A., Jiang, D., Xu, X.: A new existence theory for positive periodic solutions to functional differential equations. Comput. Math. Appl. 47, 1257–1262 (2004)MathSciNetCrossRefMATH
6.
Zurück zum Zitat Ye, D., Fan, M., Wang, H.Y.: Periodic solutions for scalar functional differential equations. Nonlinear Anal. 62, 1157–1181 (2005)MathSciNetCrossRefMATH Ye, D., Fan, M., Wang, H.Y.: Periodic solutions for scalar functional differential equations. Nonlinear Anal. 62, 1157–1181 (2005)MathSciNetCrossRefMATH
7.
Zurück zum Zitat Zeng, Z.J., Bi, L., Fan, M.: Existence of multiple positive periodic solutions for functional differential equations. J. Math. Anal. Appl. 325, 1378–1389 (2007)MathSciNetCrossRefMATH Zeng, Z.J., Bi, L., Fan, M.: Existence of multiple positive periodic solutions for functional differential equations. J. Math. Anal. Appl. 325, 1378–1389 (2007)MathSciNetCrossRefMATH
8.
Zurück zum Zitat Zhang, H.T., Li, Y.K.: Existence of positive periodic solutions for functional differential equations with impulse effects on time scales. Commun. Nonlinear Sci. Numer. Sim. 14, 19–26 (2009)CrossRefMathSciNetMATH Zhang, H.T., Li, Y.K.: Existence of positive periodic solutions for functional differential equations with impulse effects on time scales. Commun. Nonlinear Sci. Numer. Sim. 14, 19–26 (2009)CrossRefMathSciNetMATH
9.
Zurück zum Zitat Zhang, N., Dai, B.X., Qian, X.Z.: Periodic solutions for a class of higher-dimension functional differential equations with impulses. Nonlinear Anal. 68(3), 629–638 (2008)MathSciNetCrossRefMATH Zhang, N., Dai, B.X., Qian, X.Z.: Periodic solutions for a class of higher-dimension functional differential equations with impulses. Nonlinear Anal. 68(3), 629–638 (2008)MathSciNetCrossRefMATH
10.
Zurück zum Zitat Hilger, S.: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)MathSciNetCrossRefMATH Hilger, S.: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)MathSciNetCrossRefMATH
11.
Zurück zum Zitat Aulbach, B., Hilger, S.: Linear Dynamical Processes with Inhomogeneous Time Scale. Nonlinear Dynamics and Quantum Dynamical Systems. Akademie, Berlin (1990)MATH Aulbach, B., Hilger, S.: Linear Dynamical Processes with Inhomogeneous Time Scale. Nonlinear Dynamics and Quantum Dynamical Systems. Akademie, Berlin (1990)MATH
12.
Zurück zum Zitat Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Application. Birkhäuser, Boston (2001)CrossRefMATH Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Application. Birkhäuser, Boston (2001)CrossRefMATH
13.
Zurück zum Zitat Lakshmikantham, V., Sivasundaram, S., Kaymakcalan, B.: Dynamic Systems on Measure Chains. Kluwer Academic Publishers, Dordrecht (1996)CrossRefMATH Lakshmikantham, V., Sivasundaram, S., Kaymakcalan, B.: Dynamic Systems on Measure Chains. Kluwer Academic Publishers, Dordrecht (1996)CrossRefMATH
14.
Zurück zum Zitat Krasnoselskii, M.A.: Positive Solution of Operator Equation. Noorhoff, Groningen (1964) Krasnoselskii, M.A.: Positive Solution of Operator Equation. Noorhoff, Groningen (1964)
Metadaten
Titel
Multiple periodic solutions of functional differential equations with impulses on time scales
verfasst von
Zhijun Zeng
Publikationsdatum
01.02.2016
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Applied Mathematics and Computing / Ausgabe 1-2/2016
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI
https://doi.org/10.1007/s12190-015-0875-9

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