This paper is devoted to studying the following nonlinear fractional problem: 0.1 $$ \textstyle\begin{cases} (-\Delta )^{s}u+u=K( \vert x \vert )u^{p},\quad u>0, x\in {\mathbb{R}}^{N}, \\ u(x)\in H^{s}({\mathbb{R}}^{N}), \end{cases} $$ where $N\geq 3$ , $0< s<1$ , $1< p<\frac{N+2s}{N-2s}$ , $K(|x|)$ is a positive radical function. We constructed infinitely many non-radial solutions of the new type which have a more complex concentration structure for (0.1).

中文翻译：

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构造分数阶薛定谔方程的新型解

本文致力于研究以下非线性分数问题： 0.1 $$ \textstyle\begin{cases} (-\Delta )^{s}u+u=K( \vert x \vert )u^{p},\ quad u>0, x\in {\mathbb{R}}^{N}, \\ u(x)\in H^{s}({\mathbb{R}}^{N}), \end{ case} $$ where $N\geq 3$ , $0< s<1$ , $1< p<\frac{N+2s}{N-2s}$ , $K(|x|)$ 是正根函数. 我们构造了无限多个新类型的非径向解，它们对 (0.1) 具有更复杂的浓度结构。