Nontrivial solutions of Hammerstein integral equations with reflections

TL;DR

This paper uses fixed point index theory to prove new results on the existence of nonzero solutions for Hammerstein integral equations with reflections, with applications to boundary value problems.

Contribution

It introduces novel existence results for solutions of integral equations with reflections, expanding the theoretical understanding in this area.

Findings

Established conditions for nonzero solutions

Applied results to periodic boundary value problems

Extended fixed point index methods to reflected equations

Abstract

Using the theory of fixed point index, we establish new results for the existence of nonzero solutions of Hammerstein integral equations with reflections. We apply our results to a first order periodic boundary value problem with reflections.