We consider strongly coupled competitive elliptic systems that arise in the study of two-component Bose-Einstein condensates. As the coupling parameter tends to infinity, solutions that remain uniformly bounded are known to converge to a segregated limiting profile, with the difference of its components satisfying a limit scalar PDE. In the case of radial symmetry, under natural non-degeneracy assumptions on a solution of the limit problem, we establish by a perturbation argument its persistence as a solution to the elliptic system.

中文翻译：

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大耦合参数的双分量径向 Gross-Pitaevskii 系统解的构造

我们考虑在双组分玻色-爱因斯坦凝聚体的研究中出现的强耦合竞争椭圆系统。由于耦合参数趋于无穷大，已知保持一致有界的解会收敛到分离的极限轮廓，其分量的差异满足极限标量偏微分方程。在径向对称的情况下，在极限问题解的自然非简并假设下，我们通过微扰论证建立其作为椭圆系统解的持久性。