In this paper, we consider the uniqueness of nontrivial positive radial solutions to the following Schrödinger system with linear and nonlinear couplings:$\{\begin{array}{cc}\hfill & -△u_1+V_1(x)u_1={\mu }_1{u}_1^3+\beta u_1{u}_2^2+\kappa u_2\text{in}{\mathbb{R}}^N,\hfill \\ \hfill & -△u_2+V_2(x)u_2={\mu }_2{u}_2^3+\beta u_1^2{u}_2+\kappa u_1\text{in}{\mathbb{R}}^N,\hfill \\ \hfill & u_1(x),u_2(x)>0\text{in}{\mathbb{R}}^N(N\le 3),\hfill \\ \hfill & u_1(x),u_2(x)\to 0\text{ as}|x|\to \infty .\hfill \end{array}$ By using the a priori estimate technique, we obtain interesting uniqueness results for two cases: (1) sufficiently small $\beta ,\kappa >0$, (2) large $\beta >0$.

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具有线性和非线性耦合的薛定谔系统的正解的唯一性

在本文中，我们考虑以下具有线性和非线性耦合的薛定谔系统的非平凡正径向解的唯一性：$\{\begin{array}{cc}\hfill & -△{你}_1+{伏}_1(X){你}_1={\mu }_1{你}_1^3+\beta {你}_1{你}_2^2+\kappa {你}_2\text{在}{\mathbb{电阻}}^N,\hfill \\ \hfill & -△{你}_2+{伏}_2(X){你}_2={\mu }_2{你}_2^3+\beta {你}_1^2{你}_2+\kappa {你}_1\text{在}{\mathbb{电阻}}^N,\hfill \\ \hfill & {你}_1(X),{你}_2(X)>0\text{在}{\mathbb{电阻}}^N(N\le 3),\hfill \\ \hfill & {你}_1(X),{你}_2(X)\to 0\text{ 作为}|X|\to \infty .\hfill \end{array}$ 通过使用先验估计技术，我们在两种情况下获得了有趣的唯一性结果：（1）足够小 $\beta ,\kappa >0$, (2) 大 $\beta >0$.