On a semilinear elliptic systems in Hyperbolic space

Haiyang He

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arXiv · 1206.3952

On a semilinear elliptic systems in Hyperbolic space

Haiyang He

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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.

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Haiyang He. 2012-06-18. On a semilinear elliptic systems in Hyperbolic space. https://arxiv.org/abs/1206.3952

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