Some Estimates of the Norm of Solutions of Nonlinear Elliptic Eigenvalue Problems

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Abstract

We obtain estimates on the possible growth or decay rates as λ → 0 of sup |u λ |, where u λ ≠ 0 satisfies the nonlinear elliptic boundary value problem lu λ = λ f(x,u λ) in a bounded domain subject to homogeneous Dirichlet boundary conditions. The estimates generalize existing results by allowing f(x,0)≠ 0. The analysis is based on integration by parts and Sobolev inequalities.

Original languageEnglish (US)
Pages (from-to)101-109
Number of pages9
JournalApplicable Analysis
Volume18
Issue number1-2
DOIs
StatePublished - Jan 1 1984

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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