%0 Journal Article %T 具有上临界指数的p-Choquard方程基态解的存在性
Existence of Ground State Solution for p-Choquard Equation with Upper Critical Exponent %A 李银莹 %J Pure Mathematics %P 114-126 %@ 2160-7605 %D 2025 %I Hans Publishing %R 10.12677/pm.2025.154115 %X 该文讨论下列具有上临界指标的p-Choquard方程

{\begin{cases} - Δ_{p} u + V (x) {| u |}^{p - 2} u = [{(- Δ^{D})}^{\frac{- α}{2}} * {| u |}^{p_{α}^{*}}] {| u |}^{p_{α}^{*} - 2} u, i n ℝ^{N}; \\ u \in W^{1, p} (ℝ^{N}), \end{cases}

其中

N \geq 3

，

p_{α}^{*} = \frac{p}{2} (\frac{N + α}{N - p})

是关于Hardy-Littlewood-Sobolev不等式的上临界指数，

p-Choquard方程，
%K 上临界指数，
%K 基态解，
%K Nehari流形，
%K 山路引理

p-Choquard Equation %K Upper Critical Exponent %K Ground State Solution %K Nehari Manifold %K Mountain Pass Lemma %U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=111817