On some nonlinear equations with critical exponents

Haïm Brezis, Michel Willem

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Consider the problem{(- Δ u + f (frac(| x |, λ)) frac(u, λ2) = | u |frac(4, N - 2) u, in B1,; u = 0, on ∂ B1,) where B1 denotes the open unit ball in RN, N ≥ 3 and λ > 0. Under some general assumptions on f, we prove the existence or the non-existence of radial solutions. We consider also the case when λ is determined.

Original languageEnglish (US)
Pages (from-to)2286-2298
Number of pages13
JournalJournal of Functional Analysis
Volume255
Issue number9
DOIs
StatePublished - Nov 1 2008

All Science Journal Classification (ASJC) codes

  • Analysis

Keywords

  • Critical exponents
  • Elliptic equations
  • Radial solutions
  • Variational identity

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