In this paper we study the following fractional nonlinear Schrödinger equation ${\epsilon }^{2s}(-\mathrm{\Delta }{)}^{s}v+V(x)v=K(x)f(v),x\in {\mathbb{R}}^N$ where ε is a positive parameter, $s\in (0,1)$, N>2s, $V(x)$ and $K(x)$ are positive continuous functions. Using the variational techniques, we construct a family of positive solutions under general conditions on f. Moreover, we show that the solutions concentrate around the isolated components of positive local minima of the corresponding ground energy function as ε tends to zero.

中文翻译：

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具有一般非线性的分数非线性薛定谔方程的多峰解

在本文中，我们研究了以下分数非线性薛定谔方程${\epsilon }^{2s}(-\mathrm{\Delta }{)}^{s}v+五(X)v=ķ(X)F(v),X\in {\mathbb{R}}^{ñ}$其中ε是一个正参数，$s\in (0,1)$, N >2秒,$五(X)$和$ķ(X)$是正连续函数。使用变分技术，我们在f的一般条件下构造了一系列正解。此外，我们表明，当ε趋于零时，解决方案集中在相应地面能量函数的正局部最小值的孤立分量周围。