SYMMETRY AND EXISTENCE OF SOLUTIONS OF SEMI-LINEAR ELLIPTIC SYSTEMS IN HYPERBOLIC SPACE
SYMMETRY AND EXISTENCE OF SOLUTIONS OF SEMI-LINEAR ELLIPTIC SYSTEMS IN HYPERBOLIC SPACE
复制标题
双曲空间中半线性椭圆系统解的对称性和存在性
DOI：
10.1017/s0017089514000457
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发表时间：
2014
影响因子：
0.5
通讯作者：
Haiyang He
中科院分区：
文献类型：
--
作者：
Haiyang He
Abstract (0.1)
\begin{equation}\label{eq:0.1}
\left\{
\begin{array}{ll}
\displaystyle
-\Delta_{\mathbb{H}^{N}}u=|v|^{p-1}v x, \\
\displaystyle
-\Delta_{\mathbb{H}^{N}}v=|u|^{q-1}u, \\
\end{array}
\right.
\end{equation}
in the whole Hyperbolic space ℍN. We establish decay estimates and symmetry properties of positive solutions. Unlike the corresponding problem in Euclidean space ℝN, we prove that there is a positive solution pair (u, v) ∈ H1(ℍN) × H1(ℍN) of problem (0.1), moreover a ground state solution is obtained. Furthermore, we also prove that the above problem has a radial positive solution.
Abstract (0.1)
\begin{equation}\label{eq:0.1}
\left\{
\begin{array}{ll}
\displaystyle
-\Delta_{\mathbb{H}^{N}}u=|v|^{p-1}v x, \\
\displaystyle
-\Delta_{\mathbb{H}^{N}}v=|u|^{q-1}u, \\
\end{array}
\right.
\end{equation}
in the whole Hyperbolic space ℍN. We establish decay estimates and symmetry properties of positive solutions. Unlike the corresponding problem in Euclidean space ℝN, we prove that there is a positive solution pair (u, v) ∈ H1(ℍN) × H1(ℍN) of problem (0.1), moreover a ground state solution is obtained. Furthermore, we also prove that the above problem has a radial positive solution.