This work studies the existence of positive solutions for fractional Schrödinger equations of the form

$$\begin{aligned} (-\Delta )^s u + V(x) u = g(u)+\lambda |u|^{q-2}u\quad \text{ in }\quad {\mathbb {R}}^N, \end{aligned}$$

where \(s\in (0,1)\), \(N>2s\), \(V:{\mathbb {R}}^N\rightarrow {\mathbb {R}}\) is a potential function which can vanish at infinity, \(g:{\mathbb {R}}\rightarrow {\mathbb {R}}\) is superlinear and has subcritical growth, the exponent \(q\ge 2^*_s:=2N/(N-2s)\) and \(\lambda \) is a nonnegative parameter. Our approach is based on a truncation argument in combination with variational techniques and the Moser iteration method.

中文翻译：

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分数阶薛定ding方程涉及无限大处的势消失和超临界指数

这项工作研究形式为分数的薛定ding方程的正解的存在

$$ \ begin {aligned}（-\ Delta）^ su + V（x）u = g（u）+ \ lambda | u | ^ {q-2} u \ quad \ text {in} \ quad {\ mathbb {R}} ^ N，\ end {aligned} $$

其中\（s \ in（0,1）\），\（N> 2s \），\（V：{\ mathbb {R}} ^ N \ rightarrow {\ mathbb {R}} \）是一个潜在函数其可以在无限远处消失，\（克：{\ mathbb {R}} \ RIGHTARROW {\ mathbb {R}} \）是超线性和具有亚临界生长，指数\（q \ GE 2 ^ * _ S：= 2N / （N-2s）\）和\（\ lambda \）是非负参数。我们的方法基于截断参数，结合了变分技术和Moser迭代方法。