Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero with Applications
نویسنده
چکیده
We develop a nonlinear Fredholm alternative theory involving k-ball and k-set perturbations of general homeomorphisms as well as of homeomorphisms that are nonlinear Fredholm maps of index zero. Various generalized first Fredholm theorems are given and finite solvability of general (odd) Fredholm maps of index zero is 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 recent degree theories for nonlinear CFredholm maps of index zero and their perturbations.
منابع مشابه
Homeomorphisms and Finite Solvability of Their Perturbations for Fredholm Maps of Index Zero with Applications
We prove a number of homeomorphism results for nonlinear Fredholm maps of index zero and their perturbations. Moreover, we show that k-ball and k-set perturbations of these homeomorphisms are again homeomorphisms or that the corresponding equations are finitely solvable. Various generalized first Fredholm theorems are given and finite solvability of general ( odd ) Fredholm maps is also studied...
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