The differential equations on time scales through impulsive differential equations |
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Authors: | MU Akhmet M Turan |
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Institution: | 1. Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey;2. Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey |
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Abstract: | 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, Birkhäuser 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. |
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Keywords: | 34A37 34A30 34C25 34C27 |
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