# Eigenvalue problems for Fredholm operators with set-valued perturbations

## TL;DR

This paper develops a degree theory approach to analyze how eigenvalues and eigenvectors of Fredholm operators persist under set-valued perturbations, leading to bifurcation results and applications to differential inclusions.

## Contribution

It introduces a novel degree theory method to study eigenvalue persistence and bifurcation for set-valued perturbations of Fredholm operators in Banach spaces.

## Key findings

- Persistence of eigenvalues and eigenvectors under set-valued perturbations
- Existence of bifurcation points in nonlinear inclusion problems
- Applications to differential inclusions

## Abstract

By means of a suitable degree theory, we prove persistence of eigenvalues and eigenvectors for set-valued perturbations of a Fredholm linear operator. As a consequence, we prove existence of a bifurcation point for a non-linear inclusion problem in abstract Banach spaces. Finally, we provide applications to differential inclusions.