In this paper, we study a class of non-autonomous lower critical fractional Choquard equation with a pure-power nonlinear perturbation. Under some reasonable assumptions on the potential function h, we prove the existence and discuss asymptotic behavior of ground state solutions for our problem. Meanwhile, we also prove that the number of normalized solutions is at least the number of global maximum points of h when \(\varepsilon \) is small enough.

中文翻译：

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非自治分式HLS下临界Choquard方程归一化解的存在性、多重性和渐近行为

在本文中，我们研究了一类具有纯幂非线性扰动的非自治下临界分数式Choquard 方程。在对势函数h的一些合理假设下，我们证明了我们问题的基态解的存在性并讨论了渐近行为。同时，我们还证明了当\(\varepsilon \)足够小时，归一化解的数量至少为h的全局极大点的数量。