An Averaging Method for Singularly Perturbed Systems of Semilinear Differential Inclusions with C0-Semigroups |
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Authors: | Mikhail Kamenskii and Paolo Nistri |
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Institution: | (1) Dept. of Mathematics, Voronezh State University, Voronezh, Russia;(2) Dip. di Ingegneria dell'Informazione, Università di Siena, Via Roma 56, 53100 Siena, Italy |
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Abstract: | 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. |
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Keywords: | periodic solutions averaging method differential inclusions singularly perturbed system C
0-semigroups |
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