Nodal solutions of semilinear elliptic equations with critical exponent

Gabriella Tarantello, Haim Brezis

Research output: Contribution to journalArticle

44 Scopus citations

Abstract

Let Ω ⊂ RN be a bounded open set with smooth boundary and p = 2N/(N -2) be the critical Sobolev exponent. In this note we extend the results of [10] and [21] concerning nodal solutions (i.e., a solution which changes sign) for the Dirichlet problem: -Δu = |u|P-2 u + λu on Ω and u = 0 on ∂Ω, when N ≥ 6 and λ ∈ (0, λ1) with λ1 the first eigenvalue of -Δ. in H10(Ω). Similarly, for the problem -Δu = |u|P-2 u + λ|u|q-2 u on Ω and u = 0 on ∂Ω we obtain a nodal solution when λ > 0, (N + 2)/(N-2) < q < 2N/(N-2) for N = 3, 4, 5 and 2 < q < 2N/(N-2) for N ≥ 6.

Original languageEnglish (US)
Pages (from-to)25-42
Number of pages18
JournalDifferential and Integral Equations
Volume5
Issue number1
StatePublished - Jan 1 1992

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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