Existence and nonexistence results for positive solutions of an integral boundary value problem

This paper deals with the existence and nonexistence of positive solutions for the integral boundary value problem {−(au′)′+bu=g(t)f(t,u),(cosγ0)u(0)−(sinγ0)u′(0)=∫01u(τ)dα(τ),(cosγ1)u(1)+(sinγ1)u′(1)=∫01u(τ)dβ(τ). We provide sufficient conditions for the existence of either none, or one, or more positive solutions of the above problem. The main tool used in the proofs of existence results is a fixed point theorem in a cone, due to Krasnoselskii and Zabreiko. The results presented substantially unify and extend the existing results in the literature.