Singular integral equations and applications to nonlinear conjugate problems
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Chu, Jifeng; O'Regan, Donal (2010). Singular integral equations and applications to nonlinear conjugate problems. Taiwanese Journal of Mathematics 14 (2), 329-345
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.