A note on a class of higher order conformally covariant equations

Sun Yung Alice Chang, Wenxiong Chen

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

In this paper, we study the higher order conformally covariant equation (- Δ)n/2 w = (n - 1)!enw x ∈ Rn for all even dimensions n. Let a = 1/|Sn| ∫Rn enw dx. We prove, for every 0 < a < 1, the existence of at least one solution. In particular, for n = 4, we obtain the existence of radial solutions.

Original languageEnglish (US)
Pages (from-to)275-281
Number of pages7
JournalDiscrete and Continuous Dynamical Systems
Volume7
Issue number2
DOIs
StatePublished - 2001

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Keywords

  • Conformally covariant equations
  • Higher order semilinear elliptic equations
  • Non-uniqueness
  • Variational method

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