Principal eigenvalues for problems with indefinite weight function on rn

K. J. Brown, C. Cosner, J. Fleckinger

Research output: Contribution to journalArticle

64 Scopus citations

Abstract

We investigate the existence of positive principal eigenvalues of the problem − Δu(x) = λg(x)u for x ϵ Rn; u(x) → 0 as x → ∞ where the weight function g changes sign on Rn. It is proved that such eigenvalues exist if g is negative and bounded away from 0 at ∞ or if n ≥ 3 and |g(x)| is sufficiently small at ∞ but do not exist if n = 1 or 2.

Original languageEnglish (US)
Pages (from-to)147-155
Number of pages9
JournalProceedings of the American Mathematical Society
Volume109
Issue number1
DOIs
StatePublished - May 1990

Keywords

  • Elliptic boundary value problems
  • Indefinite weight function
  • Spectral theory

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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