Abstract

In this paper, we investigate the following a class of Choquard equation \begin{document}$\begin{equation*} -Δ u+u = (I_α*F(u))f(u) {\rm in} \mathbb{R}^N,\end{equation*}$ \end{document} where \begin{document}$N≥ 3,~α∈ (0,N),~I_α$\end{document} is the Riesz potential and \begin{document}$F(s) = ∈t_{0}^{s}f(t)dt$\end{document} . If \begin{document}$f$\end{document} 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.

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