On a class of nonlinear integral equations

Abstract

In this paper we consider abstract equations of the typeK ν ν +ν =w 0, in a closed convex subset of a separable Hilbert spaceH. For eachv in the closed convex subset,K v :H →H is a bounded linear map. As an application of our abstract result we obtain an existence result for nonlinear integral equations of the typeν(s)+ν(s)∫ 0 1 k(s,t)ν(t)dt =W 0(s) in the spaceL 2 [0,1].