Multiple solutions for a degenerate elliptic equation involving sublinear terms at infinity

Alexandru Kristály, Csaba Varga

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Some multiplicity results are presented for the eigenvalue problem(Pλ, μ){(- div (| x |- 2 a ∇ u) = λ | x |- 2 b f (u) + μ | x |- 2 c g (u), in Ω,; u = 0, on ∂ Ω,) where Ω ⊂ Rn(n ≥ 3) is an open bounded domain with smooth boundary, 0 ∈ Ω, 0 < a < frac(n - 2, 2), a ≤ b, c < a + 1, and f : R → R is sublinear at infinity and superlinear at the origin. Various cases are treated depending on the behaviour of the nonlinear term g.

Original languageEnglish
Pages (from-to)139-148
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume352
Issue number1
DOIs
Publication statusPublished - Apr 1 2009

Keywords

  • Caffarelli-Kohn-Nirenberg inequality
  • Degenerate elliptic problem
  • Sublinearity at infinity

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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