# American Institute of Mathematical Sciences

January  2016, 36(1): 499-508. doi: 10.3934/dcds.2016.36.499

## Radial sign-changing solution for fractional Schrödinger equation

 1 Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, P.O. Box 71010, Wuhan 430071, China

Received  January 2014 Revised  December 2014 Published  June 2015

We study the existence of a radial sign-changing solution for the stationary fractional Schrödinger equation $$\nonumber (-\Delta)^\alpha u + u=|u|^{p-1}u,\ x\in \mathbb{R}^N, N\geq 2.~~~~~~~~~~~~~{\rm (FS)}$$ where $\alpha\in (0,1)$ and $p\in(1,2_\alpha^*-1)$, $2_\alpha^*=\frac{2N}{N-2\alpha}$. By using Brouwer degree theory and variational method, we prove that there exists a radial sign-changing solution of (FS).
Citation: Zhengping Wang, Huan-Song Zhou. Radial sign-changing solution for fractional Schrödinger equation. Discrete & Continuous Dynamical Systems, 2016, 36 (1) : 499-508. doi: 10.3934/dcds.2016.36.499
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