Partial symmetry and existence of least energy solutions to some nonlinear elliptic equations on Riemannian models

Elvise Berchio, Alberto Ferrero, Maria Vallarino

Research output: Contribution to journalArticlepeer-review

Abstract

We consider least energy solutions to the nonlinear equation -Δgu=f(r,u) posed on a class of Riemannian models (M,g) of dimension n≥2 which include the classical hyperbolic space Hn as well as manifolds with unbounded sectional geometry. Partial symmetry and existence of least energy solutions is proved for quite general nonlinearities f(r, u), where r denotes the geodesic distance from the pole of M.

Original languageEnglish
Pages (from-to)1167-1193
Number of pages27
JournalNonlinear Differential Equations and Applications
Volume22
Issue number5
DOIs
Publication statusPublished - 26 Oct 2015

Keywords

  • 58J05
  • Primary 35J20
  • Secondary 35B06

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