Double positive solutions for second order nonlocal functional and ordinary boundary value problems

Abstract

In this paper we prove the existence of two positive solutions for a second order nonlinear functional nonlocal boundary value problem. The results are obtained by using a fixed point theorem on a Banach space, ordered by an appropriate cone, due to Avery and Henderson [Two positive fixed points of nonlinear operators on ordered Banach spaces, Comm. Appl. Nonlinear Anal. 8 (2001), 27–36]. Using this theorem we have the advantage that the obtained two solutions have their values at three points of their domain upper and lower bounded by a-priori given constants.