SYMMETRY AND EXISTENCE OF SOLUTIONS OF SEMI-LINEAR ELLIPTIC SYSTEMS IN HYPERBOLIC SPACE

HE, HAIYANG

Glasgow mathematical journal, Tome 57 (2015) no. 3, pp. 519-541

Résumé

(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.

Détail

DOI : 10.1017/S0017089514000457

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