Estimates for eigenfunctions and eigenvalues of nonlinear elliptic problems

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Abstract

We consider solutions to the nonlinear eigenvalue problem (*) [FORMULA PRESENT], where (*) is a quasilinear strongly coupled second order elliptic system of partial differential equations and Ω ⊆ Rn is a smooth bounded domain. We obtain lower bounds for λ in the case where f(x, u) has linear growth, and relations between λ,Ω and ess sup |u| when f(x, u) has sub- or superlinear growth. The estimates are based on integration by parts and application of certain Sobolev inequalities. We briefly discuss extensions to' higher order systems.

Original languageEnglish (US)
Pages (from-to)59-75
Number of pages17
JournalTransactions of the American Mathematical Society
Volume282
Issue number1
DOIs
StatePublished - 1984

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ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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