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

2005/08/13 by Marat Akhmet, Akhmet, Marat
Mathematics · #34A36 (Primary) 34K12 #34K13 #34K19 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:34A36 #msc:34K12 #msc:34K13 #msc:34K19

paper · pdf · doi:10.48550/arxiv.math/0508230

arxiv created 2005/08/13 · arxiv updated 2009/12/01

Abstract

In this paper we introduce a general type of differential equations with piecewise constant argument (EPCAG), and consider the problem of backward continuation of solutions. We establish the existence of global integral manifolds of quasilinear EPCAG, consisting of infinitely back continued solutions, while the solutions starting outside the invariant sets may not be back continued. 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.

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