Bifurcation for families of nonlinear perturbation of closed Fredholm operators of index zero

Abstract

In this paper we obtain a bifurcation result for parameterized families of $k$ set-contractive perturbations of closed Fredholm operators of index zero by means of an elementary degree theory and its relationship to a homotopy invariant for curves of closed Fredholm operators called the parity. This theorem is applied to the study of bifurcation of nonlinear Sturm Liouville problems on an unbounded interval.