Set-Valued Analysis

, Volume 11, Issue 4, pp 345-357

First online:

An Averaging Method for Singularly Perturbed Systems of Semilinear Differential Inclusions with C 0-Semigroups

  • Mikhail KamenskiiAffiliated withDept. of Mathematics, Voronezh State University
  • , Paolo NistriAffiliated withDip. di Ingegneria dell'Informazione, Università di Siena

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We consider a system of two semilinear differential inclusions with infinitesimal generators of C 0-semigroups. The nonlinear terms are of high frequency with respect to time and periodic with a specified period. Moreover, they are condensing in the state variables (x,y) with respect to a suitable measure of noncompactness. The goal of the paper is to give sufficient conditions to guarantee, for ∈>0 sufficiently small, the existence of periodic solutions and to study their behaviour as ∈→0. The main tool to achieve this is the topological degree theory for uppersemicontinuous, condensing vector fields.

periodic solutions averaging method differential inclusions singularly perturbed system C 0-semigroups