Existence results for a clamped beam equation with integral boundary conditions

Abstract

In this paper we investigate the existence of positive solutions of fourth-order non autonomous differential equations with integral boundary conditions, the nonlinearity is a continuous function that depends on the spatial variable and its the second-order derivative. The approach relies an extension of Krasnoselskii's fixed point theorem in a cone. Some examples are given to illustrate our results.

Keywords

• green's functions
• fourth-order boundary value problem
• integral boundary conditions
• positive solutions
• extension of krasnoselskii's fixed point theorem in a cone