We study the following nonlinear fractional Schrödinger-Poisson system with critical growth: (0.1) $$\left\{ {\begin{array}{*{20}{c}} {{{( - \Delta )}^s}u + u + \phi u = f(u) + {{\left| u \right|}^{2_s^*}}u,}&{x \in {\mathbb{R}^3},} \\ {{{( - \Delta )}^t}\phi = {u^2},\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}&{x \in {\mathbb{R}^3},} \end{array}} \right.$$ { ( − Δ ) s u + u + ϕ u = f ( u ) + | u | 2 s * − 2 u , x ∈ ℝ 3 , ( − Δ ) t ϕ = u 2 , x ∈ ℝ 3 , where 0 < s, t < 1, 2 s + 2 t >3 and $$2_s^* = {6 \over {3 - 2s}}$$ 2 s * = 6 3 − 2 s is the critical Sobolev exponent in ℝ 3 . Under some more general assumptions on f , we prove that (0.1) admits a nontrivial ground state solution by using a constrained minimization on a Nehari-Pohozaev manifold.

中文翻译：

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具有临界增长的分数阶薛定谔-泊松系统的 Nehari-Pohozaev 型基态解

我们研究以下具有临界增长的非线性分数薛定谔-泊松系统： (0.1) $$\left\{ {\begin{array}{*{20}{c}} {{{( - \Delta )}^s} u + u + \phi u = f(u) + {{\left| u \right|}^{2_s^*}}u,}&{x \in {\mathbb{R}^3},} \\ {{{( - \Delta )}^t}\phi = {u ^2},\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;}& {x \in {\mathbb{R}^3},} \end{array}} \right.$$ { ( − Δ ) su + u + ϕ u = f ( u ) + | 你| 2 s * − 2 u , x ∈ ℝ 3 , ( − Δ ) t ϕ = u 2 , x ∈ ℝ 3 , 其中 0 < s, t < 1, 2 s + 2 t >3 and $$2_s^* = {6 \over {3 - 2s}}$$ 2 s * = 6 3 − 2 s 是 ℝ 3 中的临界 Sobolev 指数。在 f 的一些更一般的假设下，我们通过在 Nehari-Pohozaev 流形上使用约束最小化来证明 (0.1) 承认一个非平凡的基态解。