Аңдатпа
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.