Abstract We study the existence of positive ground state solution for Choquard systems. In the autonomous case, we prove the existence of at least one positive ground state solution by the Pohozaev manifold method and symmetric-decreasing rearrangement arguments. Moreover, we show that each positive ground state solution is radial symmetric. While, in the nonautonomous case, a positive ground state solution is obtained by using a monotonicity trick and a global compactness lemma. We remark that, under our assumptions of the nonlinearity W u {W_{u}} , the search of ground state solutions cannot be reduced to the study of critical points of a functional restricted to a Nehari manifold.

中文翻译：

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Choquard 系统正基态解的存在性

摘要 我们研究了 Choquard 系统正基态解的存在性。在自治情况下，我们通过 Pohozaev 流形方法和对称递减重排参数证明了至少一个正基态解的存在。此外，我们表明每个正基态解都是径向对称的。而在非自治情况下，正基态解是通过使用单调性技巧和全局紧致引理获得的。我们注意到，在我们对非线性 W u {W_{u}} 的假设下，基态解的搜索不能简化为限制于 Nehari 流形的泛函临界点的研究。