Regularization method for singularly perturbed integro-differential systems with multiple spectrum

Abstract

We study the Cauchy problem for singularly perturbed integro-differential systems with multiple spectrum of the limit operator. Generalizing the idea of the regularization method developed for the asymptotic integration of systems of differential equations, asymptotic solution of the initial problem with the small parameter tends to zero. Carried regularization integro-differential problem in the case of multiple spectrum of limit operator and asymptotic invariance of space of solutions of regularized problem with respect to integral operator. Proved normal and unique solvability of iterative problems.