Regularized asymptotic solutions of integrodifferential equations with a zero operator of differential part and with several quickly varying kernels

The paper considers an integro-differential equation with the zero operator of the differential part and with several quickly changing integral kernels. The work is a continuation of the authors’ research, carried out earlier for one quickly changing integral kernel. The main ideas of such a generalization and subtleties arising in the development of the algorithm of the Lomov regularization method are fully visible in the case of two quickly changing integral kernels. After constructing an equivalent integro-differential system and its regularization, the theory of normal and unique solvability of the corresponding iterative problems is developed, which is the basis of the algorithm for constructing asymptotic solutions of the original problem.