THE INVARIANCE OF DOMAIN THEOREM FOR COMPACT PERTURBATIONS OF NONLINEAR FREDHOLM MAPS OF INDEX ZERO

Abstract

We extend the Invariance of Domain Theorem to locally compact perturbations of nonlinear Fredholm maps of index zero between Banach spaces. We show that these maps are, up to the composition with a linear isomorphism, a-contractive perturbations of the identity, where a is Kuratowski's measure of noncompactness. Thus, we prove our result using Nussbaum's degree theory.