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

This paper deals with the existence and nonexistence of positive solutions for the integral boundary value problem View the MathML source{−(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). Turn MathJax on 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.