Existence and uniqueness of positive solutions for an integral boundary value problem

Abstract

This paper deals with the existence and uniqueness of positive solutions for the second-order integral boundary value problem { u ″ + f ( u ) = 0 , u ( 0 ) = ∫ 0 1 u ( τ ) d α ( τ ) , u ( 1 ) = ∫ 0 1 u ( τ ) d β ( τ ) , where f ∈ C ( R , R ) is sign-changing. The main tools used in the proofs are the a priori estimate method and the Leray–Schauder fixed point theorem.