The differential equations on time scales through impulsive differential equations

Date

2006-12-01

Author

Akhmet, Marat

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In this paper we investigate differential equations on certain time scales with transition conditions (DETC) on the basis of reduction to the impulsive differential equations (IDE). DETC are in some sense more general than dynamic equations on time scales [M. Bohner, A. Peterson, Dynamic equations on time scales, in: An Introduction With Applications, Birkhauser Boston, Inc., Boston, MA, 2001, p. x+358; V. Laksmikantham, S. Sivasundaram, B. Kaymakcalan, Dynamical Systems on Measure Chains, in: Math. and its Appl., vol. 370, Kluwer Academic, Dordrecht, 1996]. The basic properties of linear systems, the existence and stability of periodic solutions, and almost periodic solutions are considered. Appropriate examples are given to illustrate the theory.

Subject Keywords

Differential Equations On Time Scales, Impulsive Differential Equations, Periodic Solutions, Almost Periodic Solutions, Stability

URI

https://hdl.handle.net/11511/36339

Journal

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS

DOI

https://doi.org/10.1016/j.na.2005.12.042

Collections

Department of Mathematics, Article

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Citation Formats

M. Akhmet, “The differential equations on time scales through impulsive differential equations,” NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, pp. 2043–2060, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36339.