Asymptotic solutions of a singularly perturbed integro-differential system with an unstable spectral value of exponential inhomogeneity

A. A. Bobojanov, Burkhan T. Kalimbetov, В. Ф. Сафонов

Učenye zapiski Kazanskogo gosudarstvennogo universiteta. Seriâ Fiziko-matematičeskie nauki/Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, 2026

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DOI 10.26907/2541-7746.2026.2.220-238
Data confidence 70 medium
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Abstract

This article examines an integro-differential singularly perturbed initial value problem with exponential inhomogeneity and with a spectral value that turns zero at an isolated point in time. The problem belongs to the class of singularly perturbed equations with an unstable spectrum. An algorithm is proposed for constructing an asymptotic solution of the problem based on the regularized (according to Lomov’s method) asymptotics of the fundamental solution of the corresponding homogeneous integro-differential system.