NONLINEAR SPECTRAL THEORY FOR HOMOGENEOUS OPERATORS

Abstract

We introduce and study some spectra for pairs of nonlinear operators between Banach spaces with a particular emphasis on homogeneous operators. In particular we give sucient conditions under which these spectra are closed or even compact and we show that they are purely discrete as in the linear case for compact operators. As a consequence we establish some kind of nonlinear Fredholm alternative for odd homogeneous compact perturbations of homeomorphisms and we show how this alternative applies to the eigenvalue problem for the pLaplacian.