In this article, we consider the following coupled fractional nonlinear Schrodinger system in ℝN$$\begin{cases}(-\Delta)^s u+P(x)u=\mu _1 |u|^{2p-2}u+\beta|v|^p|u|^{p-2}u, & x \in \mathbb{R}^N, \\ (-\Delta)^s v+Q(x)v=\mu_2|v|^{2p-2}v+\beta|u|^p|v|^{p-2}v, & x \in \mathbb{R}^N, \\ u, v \in H^s(\mathbb{R}^N), \end{cases}$$ where $$N \ge 2,0 0,\mu _{2} > 0$$ and β ϵ ℝ is a coupling constant. We prove that it has infinitely many non-radial positive solutions under some additional conditions on P(x), Q(x), p and β. More precisely, we will show that for the attractive case, it has infinitely many non-radial positive synchronized vector solutions, and for the repulsive case, infinitely many non-radial positive segregated vector solutions can be found, where we assume that P(x) and Q(x) satisfy some algebraic decay at infinity.

中文翻译：

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ℝN 中分数系统具有峰值的无穷多解

在本文中，我们在 ℝN$$\begin{cases}(-\Delta)^s u+P(x)u=\mu _1 |u|^{2p-2}u+ 中考虑以下耦合分数非线性薛定谔系统\beta|v|^p|u|^{p-2}u, & x \in \mathbb{R}^N, \\ (-\Delta)^s v+Q(x)v=\mu_2| v|^{2p-2}v+\beta|u|^p|v|^{p-2}v, & x \in \mathbb{R}^N, \\ u, v \in H^s( \mathbb{R}^N), \end{cases}$$ 其中 $$N \ge 2,0 0,\mu _{2} > 0$$ 和 β ϵ ℝ 是耦合常数。我们证明了在 P(x)、Q(x)、p 和 β 的一些附加条件下，它有无限多个非径向正解。更准确地说，我们将证明对于吸引情况，它有无限多个非径向正同步向量解，对于排斥情况，可以找到无限多个非径向正分离向量解，我们假设 P(x ) 和 Q(x) 在无穷远处满足一些代数衰减。