Integro-differentiated singularly perturbed equations with fast oscillating coefficients

Abstract

In the study of various issues related to dynamic stability, with the properties of media with a periodic structure, in the study of other applied problems, one has to deal with differential equations with rapidly oscillating coefficients. Asymptotic integration of differential systems of equations with such coefficients was carried out by the splitting method and the regularization method. In this paper, a system of integrodifferential equations is considered. The main objective of the study is to identify the influence of the integral term on the asymptotics of the solution to the original problem. The case of the absence of resonance is considered, i.e. the case when the integer linear combination of frequencies of the rapidly oscillating coefficient does not coincide with the frequency of the spectrum of the limit operator.