A positive fixed point theorem with applications to systems of Hammerstein integral equations

TL;DR

This paper introduces new fixed point criteria combining monotonicity and index theory, applying them to prove positive solutions for systems of nonlinear Hammerstein integral equations, supported by an illustrative example.

Contribution

It develops novel fixed point theorems that integrate monotonicity with classical index theory, specifically for systems of Hammerstein integral equations.

Findings

Established new fixed point existence criteria.

Proved positive solutions for nonlinear Hammerstein systems.

Provided an example demonstrating applicability.

Abstract

We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of positive solutions for systems of nonlinear Hammerstein integral equations. An example is also presented to show the applicability of our results.