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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1-26
Number of pages26
JournalElectronic Journal of Differential Equations
Volume2009
StatePublished - Sep 12 2009

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Fredholm alternative
  • Homeomorphism
  • Index zero
  • Nonlinear boundary conditions
  • Nonlinear fredholm mappings
  • Potential problems
  • Quasilinear elliptic equations

Fingerprint Dive into the research topics of 'Homeomorphisms and fredholm theory for perturbations of nonlinear fredholm maps of index zero with applications'. Together they form a unique fingerprint.

Cite this