Set-Valued Analysis

, Volume 11, Issue 4, pp 345–357

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

Authors

  • Mikhail Kamenskii
    • Dept. of MathematicsVoronezh State University
  • Paolo Nistri
    • Dip. di Ingegneria dell'InformazioneUniversità di Siena
Article

DOI: 10.1023/A:1025604317289

Cite this article as:
Kamenskii, M. & Nistri, P. Set-Valued Analysis (2003) 11: 345. doi:10.1023/A:1025604317289

Abstract

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 solutionsaveraging methoddifferential inclusionssingularly perturbed systemC0-semigroups

Copyright information

© Kluwer Academic Publishers 2003