Blowing-up solutions to an anisotropic Emden-Fowler equation with a singular source

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Abstract

We consider the following anisotropic Emden-Fowler equation with a singular source- div (a (x) ∇ v) = ε2 a (x) ev - 4 π α a (p) δp in Ω, v = 0 on ∂ Ω, where p ∈ Ω ⊂ R2, constant α ∈ (0, ∞) {set minus} N, a (x) is a positive smooth function and δp denotes the Dirac measure with pole at point p. If p is a local maximum point of a (x), we construct a family of solutions vε with arbitrary m bubbles concentrating at p, and the quantity ε2Ω a (x) e → 8 π (m + 1 + α) a (p).

Original languageEnglish
Pages (from-to)398-422
Number of pages25
JournalJournal of Mathematical Analysis and Applications
Volume342
Issue number1
DOIs
StatePublished - 1 Jun 2008

Keywords

  • Anisotropic Emden-Fowler equation
  • Blowing-up solutions
  • Singular source
  • Variational reduction

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