Boundary-Value Problems for Weakly Singular Integral Equations of Hammerstein Type

Abstract

We consider the problem of existence of the solution of a weakly nonlinear boundary-value problem for the Hammerstein-type integral equation with unbounded kernel, which turns, for ε = 0, into one of solutions of the generating problem. The necessary and sufficient conditions for the existence of this solution are obtained and the iterative procedure is proposed for its construction.