On the singularities of nonlinear fredholm operators of positive index

M. S. Berger, R. A. Plastock

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The singular set B = {x|F1(x) is not surjective} of a nonlinear Fredholm operator F of positive index (between Banach spaces X1 and X2) is investigated. Under the assumption that the mapping is proper and has a locally Lipschitzian Fréchet derivative F1(x), it is shown that the singular set B is nonempty. Furthermore, when the Banach spaces are infinite dimensional, B cannot be the countable union of compact sets nor can F-1(F(B)) contain isolated points.

Original languageEnglish (US)
Pages (from-to)217-221
Number of pages5
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - Jun 1980
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • Fiber bundle map
  • Higher homotopy groups
  • Nonlinear fredholm operator


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