Nontrivial solutions of systems of perturbed Hammerstein integral equations with functional terms

TL;DR

This paper investigates the existence of solutions for complex systems of perturbed Hammerstein integral equations with functional dependencies, extending to nonlocal differential equations with boundary conditions using fixed point index methods.

Contribution

It introduces new solvability results for systems with parameter-dependent nonlinearities and functional terms, applicable to nonlocal differential equations with boundary conditions.

Findings

Established conditions for existence of solutions

Applied results to nonlocal second order ODEs

Demonstrated the approach with an illustrative example

Abstract

We discuss the solvability of a fairly general class of systems of perturbed Hammerstein integral equations with functional terms that depend on several parameters. The nonlinearities and the functionals are allowed to depend on the components of the system and their derivatives. The results are applicable to systems of nonlocal second order ordinary differential equations subject to functional boundary conditions, this is illustrated in an example. Our approach is based on the classical fixed point index.