Positive solutions for a second order multi-point boundary value problem with delay

TL;DR

This paper establishes new sufficient conditions for the existence of positive solutions to a second order delay differential equation with multi-point boundary conditions, using fixed point theory.

Contribution

It improves previous results by providing broader conditions for positive solutions of multi-point boundary value problems with delays.

Findings

Sufficient conditions for positive solutions are derived.

The results extend previous work by Chen et al.

Application of Leray-Schauder fixed point theorem is demonstrated.

Abstract

In this work, we investigate the existence of positive solutions for a multi-point boundary value problem for a second order delay differential equation. Under certain growth conditions on the nonlinearity, and by the mean of Leray-Schauder fixed point theorem, sufficient conditions for the existence of nontrivial solution are obtained, which improve the results of J. Chen et al. [3].