论文标题
线性耦合的Choquard系统的归一化解决方案具有电势
Normalized solutions of linearly coupled Choquard system with potentials
论文作者
论文摘要
在本文中，我们考虑了具有潜在的线性耦合的choquard系统的解决方案\ begin {align*} \ left \ leaws {\ begin {aligned}＆ΔU+λ_1u+v_1 u+v_1（x） ＆-ΔV+λ_2v+v_2（x）v =μ_2（I_α\ star | v |^q）| V |^{q-2} u+β（x） \ int _ {\ mathbb {r}^n} u^2dx =ξ^2，〜\ \ int _ {\ mathbb {r}^n}^n} v^2dx =η^2，\ end^en^2，\ end {align {align {align*} $I_α=\frac{1}{|x|^{N-α}},~α\in(0,N),~1+\fracα{N}<p,~q<\frac{N+α}{N-2},~μ_1>0,~μ_2>0$ and $β(x)$ is a fixed function.
In this paper, we consider the existence of solutions for the linearly coupled Choquard system with potentials \begin{align*} \left\{\begin{aligned} &-Δu+λ_1 u+V_1(x)u=μ_1(I_α\star|u|^p)|u|^{p-2}u+β(x) v,\\ &-Δv+λ_2 v+V_2(x)v=μ_2(I_α\star|v|^q)|v|^{q-2}u+β(x) u, \end{aligned} \right.\quad x\in \mathbb{R}^N, \end{align*} under the constraint \begin{align*} \int_{\mathbb{R}^N}u^2dx=ξ^2,~ \int_{\mathbb{R}^N}v^2dx=η^2, \end{align*} where $I_α=\frac{1}{|x|^{N-α}},~α\in(0,N),~1+\fracα{N}<p,~q<\frac{N+α}{N-2},~μ_1>0,~μ_2>0$ and $β(x)$ is a fixed function.
