In the present paper, we are interested in the following Choquard type equation $-\Delta u+(\lambda V\left(x\right)-\mu )u=\left(I_{\alpha }\ast {\left|u\right|}^{2_{\alpha }^{\ast }}\right){\left|u\right|}^{2_{\alpha }^{\ast }-2}u+{\left|u\right|}^{p-2}u\text{in}{\mathbb{R}}^3,$where $p\in (4,6)$, $\lambda \in {\mathbb{R}}^{+}$, $\mu \in \mathbb{R}$ is a constant such that the operator $L_{\lambda }≔-\Delta +\lambda V\left(x\right)-\mu$ is non-degenerate, $I_{\alpha }$ is a Riesz potential of order $\alpha \in (0,3)$, $2_{\alpha }^{\ast }=3+\alpha$ is the upper critical exponent due to the Hardy–Littlewood–Sobolev inequality, the function $V\in C({\mathbb{R}}^3,\mathbb{R})$ is nonnegative and has a potential well $\Omega ≔\text{int}{V}^{-1}\left(0\right)$, additionally, the operator $-\Delta$ has a sequence of Dirichlet eigenvalues in $H_0^1\left(\Omega \right)$ expressed as $0<{\mu }_1<{\mu }_2<\cdots <{\mu }_n\stackrel{n}{⟶}+\infty$. If $\mu <{\mu }_1$, via the Nehari manifold techniques and the Ekeland variational principle, we prove the existence and concentration of positive ground state solutions for sufficiently large $\lambda$. If $\mu >{\mu }_1$ and $\mu \ne {\mu }_j$ for all $j\in {\mathbb{N}}_{+}$, employing the Nehari–Pankov manifold methods and the constrained minimization arguments, we obtain the existence of ground state solution for $\lambda$ large enough and verify the asymptotic behaviour of ground state solutions as $\lambda \to +\infty$.

在本文中，我们对以下Choquard型方程感兴趣 $-\Delta ü+（\lambda V（X）-\mu ）ü=（{\mathrm{一世}}_{\alpha }\ast {\left|ü\right|}^{2_{\alpha }^{\ast }}）{\left|ü\right|}^{2_{\alpha }^{\ast }-2}ü+{\left|ü\right|}^{p-2}ü\text{在}{\mathbb{[R}}^3，$哪里 $p\in （4，6）$， $\lambda \in {\mathbb{[R}}^{+}$， $\mu \in \mathbb{[R}$ 是一个常数，使得运算符 ${\mathrm{大号}}_{\lambda }≔-\Delta +\lambda V（X）-\mu$ 没有退化 ${\mathrm{一世}}_{\alpha }$ 是订单的Riesz势 $\alpha \in （0，3）$， $2_{\alpha }^{\ast }=3+\alpha$ 是由于Hardy–Littlewood–Sobolev不等式导致的最高临界指数 $V\in C（{\mathbb{[R}}^3，\mathbb{[R}）$ 是非负的并且有潜力 $\Omega ≔\text{整型}{V}^{-\mathrm{1个}}（0）$，另外，操作员 $-\Delta$ 在其中具有Dirichlet特征值序列 $H_0^{\mathrm{1个}}（\Omega ）$ 表示为 $0<{\mu }_{\mathrm{1个}}<{\mu }_2<\cdots <{\mu }_{ñ}\stackrel{ñ}{⟶}+\infty$。如果$\mu <{\mu }_{\mathrm{1个}}$通过Nehari流形技术和Ekeland变分原理，我们证明了对于足够大的正基态解的存在和集中 $\lambda$。如果$\mu >{\mu }_{\mathrm{1个}}$ 和 $\mu \ne {\mu }_{Ĵ}$ 对所有人 $Ĵ\in {\mathbb{ñ}}_{+}$，使用Nehari–Pankov流形方法和约束极小化参数，我们得到了存在基态解的 $\lambda$ 足够大并验证基态解的渐近行为 $\lambda \to +\infty$。