# Positive solutions of systems of perturbed Hammerstein integral equations with arbitrary order dependence

## TL;DR

This paper investigates the existence of positive solutions for complex systems of perturbed Hammerstein integral equations with higher order derivatives, using topological methods to extend previous results.

## Contribution

It introduces new topological techniques to establish solvability of higher order integral systems with derivative-dependent nonlinearities and functionals, broadening the scope of earlier findings.

## Key findings

- Established existence of positive solutions for a broad class of systems
- Extended previous results to include derivative-dependent nonlinearities
- Provided examples demonstrating applicability of theoretical results

## Abstract

Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral equations, where the nonlinearities and the functionals involved depend on some derivatives. We improve and complement earlier results in the literature. We also provide some examples in order to illustrate the applicability of the theoretical results.