Positive solutions of BVPs on the half-line involving functional BCs

TL;DR

This paper investigates the existence of positive solutions for second-order differential equations on the half-line with functional boundary conditions, using fixed point theory and comparison techniques.

Contribution

It introduces a novel combination of fixed point index methods and comparison results to establish positive solutions under functional boundary conditions.

Findings

Established existence criteria for positive solutions.

Extended fixed point methods to noncompact sets.

Provided new comparison results for auxiliary linear equations.

Abstract

We study the existence of positive solutions on the half-line of a second order ordinary differential equation subject to functional boundary conditions. Our approach relies on a combination between the fixed point index for operators on compact intervals, a fixed point result for operators on noncompact sets, and some comparison results for principal and nonprincipal solutions of suitable auxiliary linear equations.