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arXiv · 1904.08316

Solutions for fractional operator problem via local Pohozaev identities

Yuxia Guo·Ting Liu·Jianjun Nie
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Abstract

We consider the following fractional Schr\"{o}dinger equation involving critical exponent: \begin{equation*} \left\{\begin{array}{ll} (-\Delta)^s u+V(|y'|,y'')u=u^{2^*_s-1} \ \hbox{ in } \ \mathbb{R}^N, \\ u>0, \ y \in \mathbb{R}^N, \end{array}\right. \end{equation*} where $s\in(\frac{1}{2}, 1)$, $(y',y'')\in \mathbb{R}^2\times \mathbb{R}^{N-2}$, $V(|y'|,y'')$ is a bounded nonnegative function with a weaker symmetry condition. We prove the existence of infinitely many solutions for the above problem by a finite dimensional reduction method combining various Pohazaev identies.

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Yuxia Guo, Ting Liu, Jianjun Nie. 2019-04-17. Solutions for fractional operator problem via local Pohozaev identities. https://arxiv.org/abs/1904.08316

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