A note on existence results for a nonlinear fourth-order integral boundary value problem

TL;DR

This paper establishes new existence results for a nonlinear fourth-order boundary value problem with integral conditions, using fixed point theory, and provides examples to demonstrate their validity.

Contribution

It improves upon previous results by applying Leray-Schauder fixed point theorem to a specific nonlinear boundary value problem.

Findings

New existence results for the boundary value problem

Application of Leray-Schauder fixed point theorem

Examples confirming the theoretical results

Abstract

In this short note, we present some new existence results for a nonlinear fourth-order two-point boundary value problem with integral condition. The existence results are obtained by using the Leray-Schauder fixed point theorem. Our work improves the main results of Benaicha and Haddouchi \cite% {Benai}. In addition, examples are included to show the validity of our results.