An Averaging Method for Singularly Perturbed Systems of Semilinear Differential Inclusions with C0-Semigroups
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- Kamenskii, M. & Nistri, P. Set-Valued Analysis (2003) 11: 345. doi:10.1023/A:1025604317289
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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.