论文标题
$ \ mathbb {r}^n $中关键分数hénon方程的气泡解决方案的线性非定位和唯一性
Linear non-degeneracy and uniqueness of the bubble solution for the critical fractional Hénon equation in $\mathbb{R}^N$
论文作者
论文摘要
我们研究方程\ begin {方程*} \ label {p0}（-Δ） $ 0 <s <1 $，$α> -2S $和$ n> 2s $的分数拉普拉斯运营商。我们证明了方程式（\ ref {p0}）的径向径向对称解的线性非分类，因此，这些解决方案的唯一性结果与莫尔斯索引等于一个。特别是，基态解决方案是独一无二的。我们的非定位结果扩展在径向环境中，Dávila，del Pino和Sire所做的一些已知定理（请参阅\ cite [theorem 1.1] {davila-delpino-sire}），以及Gladiali，grossi和neves（参见\ cite \ cite \ cite [theorem 1.3] {theorem 1.3] {gladiali-i-Grossi-grossives}）。
We study the equation \begin{equation*}\label{P0} (-Δ)^s u = |x|^α u^{\frac{N+2s+2α}{N-2s}}\mbox{ in }\mathbb{R}^N,\tag{P} \end{equation*} where $(-Δ)^s$ is the fractional Laplacian operator with $0 < s < 1$, $α>-2s$ and $N>2s$. We prove the linear non-degeneracy of positive radially symmetric solutions of the equation (\ref{P0}) and, as a consequence, a uniqueness result of those solutions with Morse index equal to one. In particular, the ground state solution is unique. Our non-degeneracy result extends in the radial setting some known theorems done by Dávila, Del Pino and Sire (see \cite[Theorem 1.1]{Davila-DelPino-Sire}), and Gladiali, Grossi and Neves (see \cite[Theorem 1.3]{Gladiali-Grossi-Neves}).
