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Existence of infinitely many high energy solutions for a class of fractional Schrödinger systems
Advances in Difference Equations ( IF 3.1 ) Pub Date : 2020-06-19 , DOI: 10.1186/s13662-020-02771-1
Qi Li , Zengqin Zhao , Xinsheng Du

In this paper, we investigate a class of nonlinear fractional Schrödinger systems

$$ \left \{ \textstyle\begin{array}{l@{\quad}l}(-\triangle)^{s} u +V(x)u=F_{u}(x,u,v),& x\in \mathbb{R}^{N}, \\(-\triangle)^{s} v +V(x)v=F_{v}(x,u,v),& x\in\mathbb{R}^{N}, \end{array}\displaystyle \right . $$

where \(s\in(0, 1)\), \(N>2\). Under relaxed assumptions on \(V(x)\) and \(F(x, u, v)\), we show the existence of infinitely many high energy solutions to the above fractional Schrödinger systems by a variant fountain theorem.



中文翻译:

一类分数阶Schrödinger系统存在无穷多个高能解

在本文中,我们研究了一类非线性分数阶Schrödinger系统

$$ \ left \ {\ textstyle \ begin {array} {l @ {\ quad} l}(-\ triangle)^ {s} u + V(x)u = F_ {u}(x,u,v) ,&x \ in \ mathbb {R} ^ {N},\\(-\ triangle)^ {s} v + V(x)v = F_ {v}(x,u,v),&x \ in \ mathbb {R} ^ {N},\ end {array} \ displaystyle \ right。$$

其中\(s \ in(0,1)\)\(N> 2 \)。在\(V(x)\)\(F(x,u,v)\)的宽松假设下,我们通过变分喷泉定理证明了上述分数分数薛定ding系统存在无限多个高能解。

更新日期:2020-06-19
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