Homeomorphisms and Fredholm Theory for Perturbations of Nonlinear Fredholm Maps of Index Zero and of A-Proper Maps with Applications

P. S. Milojević ()
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P. S. Milojević: New Jersey Institute of Technology

A chapter in Approximation and Computation, 2010, pp 339-363 from Springer

Abstract: Abstract In Part I, 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 results of Sect. 1.1 are based on the Browder and Banach-Mazur homeomorphism theorems. The basic tools used in Sect. 1.2 are the recent degree theories for nonlinear C 1-Fredholm maps of index zero and their perturbations.In Part II, we discuss a number of constructive homeomorphism results for nonlinear A-proper maps and their perturbations. Error estimates are given under various conditions. We prove that k-ball and k-set perturbations of these homeomorphisms are again homeomorphisms or that the corresponding equations are finitely solvable. The theory presented in this paper is based on recent work by the author.

Keywords: Degree Theory; Projection Scheme; Ball Measure; Index Zero; Compact Perturbation (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-1-4419-6594-3_22

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DOI: 10.1007/978-1-4419-6594-3_22

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