Dimension of the set of positive solutions to nonlinear equations and applications

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Abstract

We study the covering dimension of the set of (positive) solutions to various classes of nonlinear equations involving condensing and A-proper maps. It is based on the nontriviality of the fixed point index of a certain condensing map or on oddness of a nonlinear map. Applications to nonlinear singular integral equations and to semilinear ordinary and elliptic partial differential equations are given with finite or infinite dimensional null space of the linear part.

Original languageEnglish (US)
Article number213
JournalElectronic Journal of Differential Equations
Volume2016
StatePublished - Aug 10 2016

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Condensing and A-proper maps
  • Covering dimension
  • Elliptic PDE’s
  • Exponential dichotomy
  • Fixed point index
  • Ordinary differential equations
  • Semilinear equations
  • Singular integral equations

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