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

By Matteo Bonforte, Filippo Gazzola, Gabriele Grillo and Juan Luis Vázquez

Abstract

We study the Emden-Fowler equation $-\Delta u=|u|^{p-1}u$ 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 \cite{mancini, bhakta} 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

Topics: Mathematics - Analysis of PDEs
Year: 2011
OAI identifier: oai:arXiv.org:1104.3666
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