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- W3047044580 abstract "We consider the fractional critical Schr{o}dinger equation (FCSE) begin{align*} slaplace{u}-abs{u}^{2^{ast}_{s}-2}u=0, end{align*} where $u in dot H^s( R^N)$, $Ngeq 2$, $0<s<1$ 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}." @default.
- W3047044580 created "2020-08-10" @default.
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- W3047044580 date "2020-08-05" @default.
- W3047044580 modified "2023-09-24" @default.
- W3047044580 title "Entire sign-changing solutions to the fractional critical Schr{o}dinger equation" @default.
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- W3047044580 doi "https://doi.org/10.48550/arxiv.2008.02119" @default.
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