Integral manifolds of differential equations with piecewise constant argument of generalized type


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Akhmet M. U.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.66, no.2, pp.367-383, 2007 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 66 Issue: 2
  • Publication Date: 2007
  • Doi Number: 10.1016/j.na.2005.11.032
  • Journal Name: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.367-383
  • Keywords: integral manifolds, piecewise constant argument of generalized type, differentiability of integral manifolds, periodic solutions, PERIODIC-SOLUTIONS, LINEARIZATION

Abstract

In this paper we introduce a general type of differential equations with piecewise constant argument (EPCAG). The existence of global integral manifolds of the quasilinear EPCAG is established when the associated linear homogeneous system has an exponential dichotomy. The smoothness of the manifolds is investigated. The existence of bounded and periodic solutions is considered. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Appropriate illustrating examples are given. (c) 2005 Elsevier Ltd. All rights reserved.