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：

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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）\）和\（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。