Nonlinear perturbed integral equations related to nonlocal boundary value problems

TL;DR

This paper establishes new topological results on the existence, non-existence, localization, and multiplicity of solutions for a class of nonlinear perturbed integral equations, relevant to nonlocal boundary value problems.

Contribution

It introduces novel topological methods to analyze nonlinear perturbed integral equations associated with nonlocal boundary value problems.

Findings

Proved conditions for existence and non-existence of solutions.

Identified criteria for solution localization and multiplicity.

Provided examples illustrating theoretical results.

Abstract

By topological arguments, we prove new results on the existence, non-existence, localization and multiplicity of nontrivial solutions of a class of perturbed nonlinear integral equations. These type of integral equations arise, for example, when dealing with boundary value problems where nonlocal terms occur in the differential equation and/or in the boundary conditions. Some examples are given to illustrate the theoretical results.