The differential equations on time scales through impulsive differential equations

Akhmet M. U. , Turan M.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, cilt.65, sa.11, ss.2043-2060, 2006 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 65 Konu: 11
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/
  • Sayfa Sayıları: ss.2043-2060


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. (c) 2006 Elsevier Ltd. All rights reserved.