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

  • Elvise BerchioEmail author
  • Alberto Ferrero
  • Maria Vallarino


We consider least energy solutions to the nonlinear equation \({-\Delta_g u=f(r,u)}\) posed on a class of Riemannian models (M,g) of dimension \({n \geq 2}\) which include the classical hyperbolic space \({\mathbb{H}^{n}}\) 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.

Mathematics Subject Classification

Primary 35J20 Secondary 35B06 58J05 


Riemannian models Least energy solutions Partial symmetry 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Elvise Berchio
    • 1
    Email author
  • Alberto Ferrero
    • 2
  • Maria Vallarino
    • 1
  1. 1.Dipartimento di Scienze MatematichePolitecnico di TorinoTurinItaly
  2. 2.Dipartimento di Scienze e Innovazione TecnologicaUniversità del Piemonte Orientale “Amedeo Avogadro”AlessandriaItaly

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