Upper and lower solutions for a homogeneous dirichlet problem with nonlinear diffusion and the principle of linearized stability

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3 Scopus citations

Abstract

We consider a class of quasilinear elliptic equations on a bounded domain subject to homogeneous Dirichlet boundary data. We establish a means of constructing upper and lower solutions in a neighborhood of a given solution to the quasilinear boundary value problem, leading to a principle of linearized stability instability for the solution viewed as an equilibrium to the corresponding parabolic problem.

Original languageEnglish (US)
Pages (from-to)1229-1236
Number of pages8
JournalRocky Mountain Journal of Mathematics
Volume30
Issue number4
DOIs
StatePublished - 2000

Keywords

  • Homogeneous Dirichlet problem
  • Nonlinear diffusion
  • Principle of linearized stability
  • Upper and lower solutions

ASJC Scopus subject areas

  • Mathematics(all)

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