Existence of positive solutions of a Hammerstein integral equation using the layered compression-expansion fixed point theorem

TL;DR

This paper proves the existence of positive solutions for a Hammerstein integral equation by applying the Layered Compression-Expansion Fixed Point Theorem, offering corollaries and an example for practical application.

Contribution

It introduces the use of the Layered Compression-Expansion Fixed Point Theorem to establish positive solutions for Hammerstein integral equations, expanding existing solution methods.

Findings

Existence of positive solutions under specific kernel conditions

Development of corollaries for practical application

An illustrative example demonstrating the main results

Abstract

In this paper, we show the existence of a positive solution of a Hammerstein integral equation under certain conditions on the kernel. We apply the recent Layered Compression-Expansion Fixed Point Theorem. Finally, we provide corollaries to help in application of the main results and present an example.