In this paper, we consider the following weakly coupled nonlinear Schrödinger system

$$\left\{\begin{array}{cc}-{\epsilon }^2\mathrm{\Delta }{u}_1+V_1(x)u_1=|u_1{|}^{2p-2}{u}_1+\beta |u_1{|}^{p-2}{|u_2|}^p{u}_1,\hfill & x\in {\mathbb{R}}^N,\hfill \\ -{\epsilon }^2\mathrm{\Delta }{u}_2+V_2(x)u_2=|u_2{|}^{2p-2}{u}_2+\beta |u_2{|}^{p-2}{|u_1|}^p{u}_2,\hfill & x\in {\mathbb{R}}^N,\hfill \end{array}\right.$$

where $\epsilon >0$, $\beta \in \mathbb{R}$ is a coupling constant, $2p\in (2,2^{\ast })$ with $2^{\ast }=\frac{2N}{N-2}$ if $N\ge 3$ and $+\infty$ if $N=1,2$, V₁ and V₂ belong to $C({\mathbb{R}}^N,[0,\infty ))$.

中文翻译：

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具有小耦合系数的扰动非线性薛定谔系统的非标准解

在本文中，我们考虑以下弱耦合非线性薛定谔系统

$$\left\{\begin{array}{cc}-{\epsilon }^2\mathrm{\Delta }{你}_1+{伏}_1(X){你}_1=|{你}_1{|}^{2磷-2}{你}_1+\beta |{你}_1{|}^{磷-2}{|{你}_2|}^{磷}{你}_1,\hfill & X\in {\mathbb{电阻}}^N,\hfill \\ -{\epsilon }^2\mathrm{\Delta }{你}_2+{伏}_2(X){你}_2=|{你}_2{|}^{2磷-2}{你}_2+\beta |{你}_2{|}^{磷-2}{|{你}_1|}^{磷}{你}_2,\hfill & X\in {\mathbb{电阻}}^N,\hfill \end{array}\right.$$

在哪里 $\epsilon >0$, $\beta \in \mathbb{电阻}$ 是耦合常数， $2磷\in (2,2^{＊})$ 和 $2^{＊}=\frac{2N}{N-2}$ 如果 $N\ge 3$ 和 $+\infty$ 如果 $N=1,2$, V ₁和V ₂属于$C({\mathbb{电阻}}^N,[0,\infty ))$.