Regularised asymptotic solutions of integro-differential equations with zero operator of the differential part and with rapidly oscillating inhomogeneity
Mashkhura A. Bobodzhanova, Burkhan T. Kalimbetov, В. Ф. Сафонов · Applicable Analysis · 2025
The paper considers a linear integro-differential equation with zero operator of the differential part, the right-hand side of which contains a rapid oscillation inhomogeneity. An algorithm of the Lomov regularization method is developed for equations of this type. The work is a continuation of research carried out earlier for slowly changing heterogeneity. In this case, the conditions for the solvability of the corresponding iterative problems will have the form not of differential (as was the case in problems with a non-zero operator of the differential part), but of integro-differential equations, and inhomogeneity plays an essential role in the formation of these equations.