Infinitely many solutions for a Hénon-type system in hyperbolic space
This paper is devoted to study the semilinear elliptic system of Hénon-type \begin{eqnarray*} -Δ_{\mathbb{B}^{N}}u= K(d(x))Q_{u}(u,v) \\ -Δ_{\mathbb{B}^{N}}v= K(d(x))Q_{v}(u,v) \end{eqnarray*} in the hyperbolic space $\mathbb{B}^{N}$, $N\geq 3$, where $u, v \in H_{r}^{1}(\mathbb{B}^{N})=\{ϕ\in H^1(\mathbb{B}^N): ϕ\, \text{is radial}\}$ and $-Δ_{\mathbb{B}^{N}}$ denotes the Laplace-Beltrami operator on $\mathbb{B}^N$, $Q \in C^{1}(\mathbb{R}\times \mathbb{R},\mathbb{R})$ is a p-homogeneous function, $d(x)=d_{\mathbb{B}^N}(0,x)$ and $K\geq0 $ is a continuous function. We prove a compactness result and together with the Clark's theorem we establish the existence of infinitely many solutions.
math.AP↗