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SYMMETRY AND EXISTENCE OF SOLUTIONS OF SEMI-LINEAR ELLIPTIC SYSTEMS IN HYPERBOLIC SPACE
Part of:
Partial differential equations on manifolds; differential operators
Elliptic equations and systems
Published online by Cambridge University Press: 18 December 2014
Abstract
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(0.1)
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.
\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}
MSC classification
Secondary:
35J60: Nonlinear elliptic equations
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 2014
References
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