Solutions of perturbed Hammerstein integral equations with applications

TL;DR

This paper develops topological methods to analyze solutions of perturbed Hammerstein integral equations, demonstrating their applicability to various models in applied mathematics and elliptic boundary value problems.

Contribution

It introduces new theoretical results on existence, non-existence, localization, and multiplicity of solutions for these integral equations, with applications to physical models.

Findings

Established conditions for solution existence and multiplicity.

Applied theory to models of chemical reactors, beams, and thermostats.

Proved existence of nontrivial radial solutions for elliptic boundary value problems.

Abstract

By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical results, we study some problems that occur in applied mathematics, namely models of chemical reactors, beams and thermostats. We also apply our theory in order to prove the existence of nontrivial radial solutions of systems of elliptic boundary value problems subject to nonlocal, nonlinear boundary conditions.