Nonlinear fredholm maps of index zero and their singularities

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18 Scopus citations

Abstract

Let F: X → Y be a C1 Fredholm map of index zero between two Banach spaces. Defining the singular set B = (x|F′(x) is not surjective), we study the local and global effect of B on the map F. In particular it is shown that if b ∊ B is isolated in B, then, for dim X and dim Y ≥ 3, F is a local homeomorphism at b. We then show that if B consists of discrete points, F is a global homeomorphism of X onto Y. A nonlinear partial differential equation is included as an illustration.

Original languageEnglish (US)
Pages (from-to)317-322
Number of pages6
JournalProceedings of the American Mathematical Society
Volume68
Issue number3
DOIs
StatePublished - Mar 1978

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Covering space map
  • Fredholm map of index zero
  • Proper

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