On the dimension and the index of the solution set of nonlinear equations

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Abstract

We study the covering dimension and the index of the solution set to multiparameter nonlinear and semilinear operator equations involving Fredholm maps of positive index. The classes of maps under consideration are (pseudo) ^-proper and either approximation-essential or equivariant approximation- essential. Applications are given to semilinear elliptic BVP's.

Original languageEnglish (US)
Pages (from-to)835-856
Number of pages22
JournalTransactions of the American Mathematical Society
Volume347
Issue number3
DOIs
StatePublished - Mar 1995

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • (pseudo) A-proper maps
  • Approximation-essential maps
  • Covering dimension
  • Elliptic BVP’s
  • Equivariant maps
  • Index
  • Multiparameter continuation problems

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