论文标题
分数关键schr {Ö} dinger方程的整个签名解决方案
Entire sign-changing solutions to the fractional critical Schr{ö}dinger equation
论文作者
论文摘要
我们考虑分数批判性schr {Ö} dinger方程（fcse）\ begin {align*} \ \ slaplace {u} - \ abs { $ 2^{\ ast} _ {s} = \ frac {2n} {n-2s} $。借助Mini-Max理论和具有模棱两可的群体作用的浓度紧凑性原理，我们在能量空间$ \ dot h^s（\ r^n）$中获得了（fcse）的（fcse）的新型非radial，sign-sign-sign-sign-sign-sign-sign-sign-sign-sign-sign-sign-sign-sign-sign-sign的变化。关键组成部分是，我们使用Equivariant组将$ \ dot h^s（\ r^n）$分成几个连接的组件，然后结合浓度紧凑的参数，以在每个组件中显示palais-smale序列的紧凑属性，并在$ \ dot h^s（fcse）中获得许多解决方案（fcse）。这里的解决方案和论点都与Garrido，Musso，\ cite {Gm2016pjm}的Musso以及Abreu，Barbosa和Ramirez在\ Cite {ABR2019ARXIV}中不同的解决方案不同。
We consider the fractional critical Schr{ö}dinger equation (FCSE) \begin{align*} \slaplace{u}-\abs{u}^{2^{\ast}_{s}-2}u=0, \end{align*} where $u \in \dot H^s( \R^N)$, $N\geq 2$, $0<s<1$ and $2^{\ast}_{s}=\frac{2N}{N-2s}$. By virtue of the mini-max theory and the concentration compactness principle with the equivariant group action, we obtain the new type of non-radial, sign-changing solutions of (FCSE) in the energy space $\dot H^s(\R^N)$. The key component is that we use the equivariant group to partion $\dot H^s(\R^N)$ into several connected components, then combine the concentration compactness argument to show the compactness property of Palais-Smale sequences in each component and obtain many solutions of (FCSE) in $\dot H^s(\R^N)$. Both the solutions and the argument here are different from those by Garrido, Musso in \cite{GM2016pjm} and by Abreu, Barbosa and Ramirez in \cite{ABR2019arxiv}.
