Eigenvalue Problems for Fredholm Operators with Set-Valued Perturbations

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.

Keywords

• fredholm operators
• eigenvalue problems
• set-valued maps
• 47j10
• 47h11
• 58c06