Existence and nonexistence results for fifth-order multi-point boundary value problems involving integral boundary condition

Abstract

In this paper, by using the classical compression-expansion fixed point theorem of Krasnoselskii, we study the existence and nonexistence of monotone and convex positive solutions for a nonlinear fifth-order differential equation with multi-point and integral boundary condition. We establish some sufficient conditions for the existence of at least one or two monotone and convex  positive solutions. Furthermore, the nonexistence results of positive solution are also considered. As applications, two examples are presented to illustrate the validity of our main results.