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

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

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.


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