Singular integral equations and applications to nonlinear conjugate problems

Abstract

In this paper, we establish the existence of multiple positive solutions for singular integral equations. The proof is based on a general existence principle established using a nonlinear alternative principle of Leray-Schauder type and a well-known fixed point theorem in cones. As an application, we consider higher order nonlinear singular conjugate boundary value problems. Some recent results in the literature are generalized and improved.