In this paper we investigate the existence of a positive vector solution for a class of non-linear strongly coupled Schrödinger system in \(\mathbb{R}^N\), which is non-autonomous and asymptotically linear at infinity. Using topological arguments, combined with sharp exponential decay estimates, we obtain a bound state solution when the ground state is not attained.

中文翻译：

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具有饱和的强耦合非线性Schrödinger系统的束缚态

本文研究\（\ mathbb {R} ^ N \）中的一类非线性强耦合Schrödinger系统正向量解的存在性，该系统在无穷远处是非自治的且渐近线性的。使用拓扑参数，结合急剧的指数衰减估计，我们可以在未获得基态时获得束缚态解。