Homeomorphisms and fredholm theory for perturbations of nonlinear fredholm maps of index zero with applications

We develop a nonlinear Fredholm alternative theory involving kball and k-set perturbations of general homeomorphisms and of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems and finite solvability of general (odd) Fredholm maps of index zero are also studied. We apply these results to the unique and finite solvability of potential and semilinear problems with strongly nonlinear boundary conditions and to quasilinear elliptic equations. The basic tools used are the Nussbaum degree and the degree theories for nonlinear C1-Fredholm maps of index zero and their perturbations.