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

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.

Cited by in corpus (1)

• On a semilinear elliptic systems in Hyperbolic space