Contrast structure in equations with zero spectrum of limit operator and irreversible spectral value of the kernel
In this paper we consider the Cauchy problem for systems of integro - differential equations at presence zeros in the spectrum of the limit operator and singularities in the integral term. Spectral singularities the integral operator gives in solving the original problem essentially singular singularities in the small parameter, which describes the inner boundary layer. For constructing mathematical theory, the formulation of the criterion of the correctness of the mathematical description of the boundary layer and the development of a regular theory for singularly perturbed problems we used the idea of regularization method. The procedure of regularization of the integral operator was Illustrated and the solvability of iterative problems was proved.