Set-Valued Analysis

, Volume 11, Issue 4, pp 345–357

An Averaging Method for Singularly Perturbed Systems of Semilinear Differential Inclusions with C0-Semigroups

  • Mikhail Kamenskii
  • Paolo Nistri


We consider a system of two semilinear differential inclusions with infinitesimal generators of C0-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 C0-semigroups 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Mikhail Kamenskii
    • 1
  • Paolo Nistri
    • 2
  1. 1.Dept. of MathematicsVoronezh State UniversityVoronezhRussia
  2. 2.Dip. di Ingegneria dell'InformazioneUniversità di SienaSienaItaly

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