Existence and non-existence of nontrivial solutions for Schrödinger systems via Nehari-Pohozaev manifold

Existence and non-existence of nontrivial solutions for Schrödinger systems via Nehari-Pohozaev manifold
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DOI：
10.1016/j.camwa.2017.08.010
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发表时间：
2017-12
期刊：
Comput. Math. Appl.
影响因子：
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通讯作者：
Dongdong Qin;Jing Chen-;Xianhua Tang
Dongdong Qin;Jing Chen-;Xianhua Tang
中科院分区：
其他
文献类型：
--
作者：
Dongdong Qin;Jing Chen-;Xianhua Tang

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本文研究了由非线性光学和玻色-爱因斯坦凝聚引起的非自治薛定谔方程的耦合梯度系统的束缚态的存在性。通过使用约束在Nehari-Pohozaev流形上的变分方法，我们得到了非负和正束缚态解的存在性。特别地，我们证明了一个极小化问题的不存在性结果。
This paper is concerned with existence of bound states for a coupled gradient system of nonautonomous Schrödinger equations which arises from studies of nonlinear optics and Bose–Einstein condensates. By using variational methods that are constrained to a Nehari–Pohozaev manifold, we obtain existence of nonnegative and positive bound states solutions. In Particular, we show non-existence result for a minimizing problem.