# American Institute of Mathematical Sciences

January  2019, 18(1): 285-300. doi: 10.3934/cpaa.2019015

## Existence of ground state solutions for Choquard equation involving the general upper critical Hardy-Littlewood-Sobolev nonlinear term

 School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

* Corresponding author

Received  November 2017 Revised  November 2017 Published  August 2018

Fund Project: The research is supported by National Natural Science Foundation of China (No.11471267).

In this paper, we investigate the following a class of Choquard equation
 $\begin{equation*} -Δ u+u = (I_α*F(u))f(u) \ \ \ \ \ \ {\rm in} \ \mathbb{R}^N,\end{equation*}$
where
 $N≥ 3,~α∈ (0,N),~I_α$
is the Riesz potential and
 $F(s) = ∈t_{0}^{s}f(t)dt$
. If
 $f$
satisfies almost necessary the upper critical growth conditions in the spirit of Berestycki and Lions, we obtain the existence of positive radial ground state solution by using the Pohožaev manifold and the compactness lemma of Strauss.
Citation: Gui-Dong Li, Chun-Lei Tang. Existence of ground state solutions for Choquard equation involving the general upper critical Hardy-Littlewood-Sobolev nonlinear term. Communications on Pure & Applied Analysis, 2019, 18 (1) : 285-300. doi: 10.3934/cpaa.2019015
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