Application of the Leray-Schauder alternative to nonlinear singular operator equations

Abstract

In this paper, we study the problem of existence of solution of nonlinear singular integral equations of the form {w(z) = Phi(z) + T(G)F (., w (.), h (.)) (z) h(z) = Phi'(z) + Pi(G)F (., w (.), h (.)) (z), z is an element of G subset of C. (C) 2009 Elsevier Ltd. All rights reserved.