Infinitely many solutions for a Hénon-type system in hyperbolic space

Abstract

This paper is devoted to studying the semilinear elliptic system of Hénon type ⎧ ⎪ ⎨ ⎪ ⎩-B N u = K(d(x))Q u (u, v),-B N v = K(d(x))Q v (u, v), u, v ∈ H 1 r (B N), N ≥ 3, in the hyperbolic space B N , where H 1 r (B N) = {u ∈ H 1 (B N) : u is radial} and-B N denotes the Laplace-Beltrami operator on B N , d(x) = d B N (0, x), Q ∈ C 1 (R × R, R) is p-homogeneous, and K ≥ 0 is a continuous function. We prove a compactness result and, together with Clark's theorem, we establish the existence of infinitely many solutions.