On a semilinear elliptic systems in Hyperbolic space

Abstract

In this paper, we consider systems of semilinear elliptic equations \displaystyle -Δ_{\mathbb{H}^{N}}u=|v|^{p-1}v, \displaystyle -Δ_{\mathbb{H}^{N}}v=|u|^{q-1}u, in the whole of Hyperbolic space ${\mathbb{H}}^N$. We establish decay estimates and symmetry properties of positive solutions. Unlike the corresponding problem in Euclidean space ${\mathbb{R}}^N$, we prove that there exists a nonnegative nontrivial solution of problem.

17pages

References in corpus (1)

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