Periodic solutions of the hybrid system with small parameter


AKHMET M., Buyukadali C., Ergenc T.

NONLINEAR ANALYSIS-HYBRID SYSTEMS, vol.2, no.2, pp.532-543, 2008 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2 Issue: 2
  • Publication Date: 2008
  • Doi Number: 10.1016/j.nahs.2006.07.005
  • Journal Name: NONLINEAR ANALYSIS-HYBRID SYSTEMS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.532-543
  • Keywords: Quasi linear differential equations, The small parameter, Piecewise constant arguments of generalized type, Periodic solutions, Stability, PIECEWISE-CONSTANT ARGUMENT, DIFFERENTIAL-EQUATIONS, GREENS-FUNCTION

Abstract

In this paper we investigate the existence and stability of the periodic solutions of a quasilinear differential equation with piecewise constant argument. The continuous and differentiable dependence of the solutions on the parameter and the initial value is considered. A new Gronwall-Bellman type lemma is proved. Appropriate examples are constructed. (c) 2007 Elsevier Ltd. All rights reserved.