论文标题
对于奇异扰动的分数Kirchhoff问题的半经典有限状态的局部唯一性
Local uniqueness of semiclassical bounded states for a singularly perturbed fractional Kirchhoff problem
论文作者
论文摘要
在本文中，我们考虑以下奇异的扰动分数Kirchhoff问题\ BEGIN {qore*} \ big（\ varepsilon^{2S} a+\ varepsilon^{4S-n} b {\ int _ {\ Mathbb {r}^{n}}}} |（-Δ）^{\ frac {s} {2} {2}} u |^2dx \ big）（ - δ）^su+v（x）^su+v（x） \ Mathbb {r}^{n}，\ end {equation*}其中$ a，b> 0 $，$ 2S <n <4S $带有$ s \ in（0,1）$，$ 2 <p <2^*_ s = _ s = \ frac {2n} {2n} {2n} {n-2s} {n-2s} {n-2s} $ and $ and $ and $ and（ - guan）对于$ \ varepsilon> 0 $，我们可以通过扩展技术建立了一种本地pohozǎEV身份，然后我们可以根据我们的最新结果基于对限制问题的唯一性和非确定解决方案的唯一结果，建立了一种本地pohozǎEV身份。
In this paper, we consider the following singularly perturbed fractional Kirchhoff problem \begin{equation*} \Big(\varepsilon^{2s}a+\varepsilon^{4s-N} b{\int_{\mathbb{R}^{N}}}|(-Δ)^{\frac{s}{2}}u|^2dx\Big)(-Δ)^su+V(x)u=|u|^{p-2}u,\quad \text{in}\ \mathbb{R}^{N}, \end{equation*} where $a,b>0$, $2s<N<4s$ with $s\in(0,1)$, $2<p<2^*_s=\frac{2N}{N-2s}$ and $(-Δ)^s$ is the fractional Laplacian. For $\varepsilon> 0$ sufficiently small and a bounded continuous function $V$, we establish a type of local Pohozǎev identity by extension technique and then we can obtain the local uniqueness of semiclassical bounded solutions based on our recent results on the uniqueness and non-degeneracy of positive solutions to the limit problem.
