Existence Results for a Nonlinear Fourth Order Ordinary Differential Equation with Four-Point Boundary Value Conditions

Abstract

The aim of this paper is to study the more accurate existence results of positive solution for a nonlinear fourth order ordinary differential equation (for short NLFOODE) using four-point boundary value conditions (for short BVCs). The upper and lower solution method and Schauder’s fixed point theorem have been applied to demonstrate the obtained existence results. First, the Green’s function of the corresponding linear boundary value problem (for short BVP) has been constructed and then it is used to solve the considered BVP of this paper. An example has also been included at the end of this paper to support the analytic proof.

Keywords

• NLFOODE with four-point BVCs
• Upper and lower solution method
• Schauder’s fixed point theorem
• Existence of positive solution

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