SOLVİNG PARTİAL INTEGRAL EQUATİONS FOR FUNCTİONS OF THREE VARİABLES WİTH DEGENERATE KERNELS

Abstract

This paper investigates the problem of solving a linear partial integral equation for functions of three variables with degenerate (separated) kernels. The existence and uniqueness of a continuous solution in the space C[a,b]³ are proved. It is shown that when the kernels are given in separated form, the problem reduces to a single-variable Fredholm integral equation of the second kind, and the solution is expressed explicitly through exact formulas. Additionally, the condition for the homogeneous equation to possess a nontrivial solution is established.