Classification of radial solutions to the Emden–Fowler equation on the hyperbolic space

  • Matteo Bonforte
  • Filippo Gazzola
  • Gabriele Grillo
  • Juan Luis Vázquez


We study the Emden–Fowler equation −Δu = |u| p−1 u on the hyperbolic space \({{\mathbb H}^n}\) . We are interested in radial solutions, namely solutions depending only on the geodesic distance from a given point. The critical exponent for such equation is p = (n + 2)/(n − 2) as in the Euclidean setting, but the properties of the solutions show striking differences with the Euclidean case. While the papers (Bhakta and Sandeep, Poincaré Sobolev equations in the hyperbolic space, 2011; Mancini and Sandeep, Ann Sci Norm Sup Pisa Cl Sci 7(5):635–671, 2008) consider finite energy solutions, we shall deal here with infinite energy solutions and we determine the exact asymptotic behavior of wide classes of finite and infinite energy solutions.

Mathematics Subject Classification (2000)

35J15 35J61 


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Matteo Bonforte
    • 1
  • Filippo Gazzola
    • 2
  • Gabriele Grillo
    • 2
  • Juan Luis Vázquez
    • 1
  1. 1.Departamento de MatemáticasUniversidad Autónoma de MadridMadridSpain
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanItaly

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