@Article{He2022,
author = "He, Haiyang",
title = "Nonlinear Choquard equations on hyperbolic space",
journal = "Opuscula Math.",
year = "2022",
volume = "42",
number = "5",
pages = "691--708",
doi = "https://doi.org/10.7494/OpMath.2022.42.5.691",
url = "https://doi.org/10.7494/OpMath.2022.42.5.691",
abstract = "In this paper, our purpose is to prove the existence results for the following nonlinear Choquard equation \[-\Delta_{\mathbb{B}^{N}}u=\int_{\mathbb{B}^N}\dfrac{|u(y)|^{p}}{|2\sinh\frac{\rho(T_y(x))}{2}|^\mu} dV_y \cdot |u|^{p-2}u +\lambda u\] on the hyperbolic space \(\mathbb{B}^N\), where \(\Delta_{\mathbb{B}^{N}}\) denotes the Laplace-Beltrami operator on \(\mathbb{B}^N\), \[\sinh\frac{\rho(T_y(x))}{2}=\dfrac{|T_y(x)|}{\sqrt{1-|T_y(x)|^2}}=\dfrac{|x-y|}{\sqrt{(1-|x|^2)(1-|y|^2)}},\] \(\lambda\) is a real parameter, \(0\lt \mu\lt N\), \(1\lt p\leq 2_\mu^*\), \(N\geq 3\) and \(2_\mu^*:=\frac{2N-\mu}{N-2}\) is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.",
keywords = "nonlinear Choquard equation, hyperbolic space, existence solutions, Hardy-Littlewood-Sobolev inequality",
issn = "1232-9274"
}