Fixed point theorem based solvability of fourth order nonlinear differential equation with four-point boundary value conditions

Abstract

In this paper, an existence criterion of nontrivial solution to the four-point boundary value problem for fourth order ordinary differential equation has been established. The analysis of this paper is based on the well-known Krasnosclskii-Zabreiko fixed point theorem. An illustrative example is included to support the analytic proof of established existence criteria.