Nonlinear Choquard equations on hyperbolic space

In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation \-₁^₍u=₁₍|u (y) |^p|2 (Tᵧ (x) ) {2|^} dVᵧ |u|^p-2u + u\ on the hyperbolic space \ (BN\), where \ (₁^₍\) denotes the Laplace-Beltrami operator on \ (BN\), \ (Tᵧ (x) ) 2=|Tᵧ (x) |1-|Tᵧ (x) |²=|x-y| (1-|x|²) (1-|y|²), \ \ (\) is a real parameter, \ (0 N\), \ (1 p 2_^*\), \ (N 3\) and \ (2_^*: =2N-N-2\) is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.