ON THE ANALYTICAL SOLUTION OF SYSTEMS OF LINEAR INTEGRAL EQUATIONS

This article analyzes the mathematical essence of systems of linear integral equations and the problems of their solution. In the course of the study, Fredholm and Volterra systems of integral equations of the second kind are considered in a general form, and the conditions for the existence of solutions as well as their main properties are described. Special attention is paid to the structure of the integral kernel, and effective methods for solving systems with separable (degenerate) kernels are demonstrated. The obtained results have significant theoretical and practical importance for the study of the theory of integral equations and for solving applied problems related to mathematical modeling. In addition, the research results can be used as a methodological resource in teaching mathematical analysis and functional analysis in higher educational institutions.