Radial sign-changing solution for fractional Schrödinger equation

Zhengping  Wang; Huan-Song Zhou

doi:10.3934/dcds.2016.36.499

Article Contents

2016, Volume 36, Issue 1: 499-508. Doi: 10.3934/dcds.2016.36.499

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Radial sign-changing solution for fractional Schrödinger equation

Zhengping Wang^1, and
Huan-Song Zhou^1,

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

Received: January 2014

Revised: December 2014

Published: May 2017

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Abstract

We study the existence of a radial sign-changing solution for the stationary fractional Schrödinger equation \begin{equation}\nonumber (-\Delta)^\alpha u + u=|u|^{p-1}u,\ x\in \mathbb{R}^N, N\geq 2.~~~~~~~~~~~~~{\rm (FS)} \end{equation} 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).

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Mathematics Subject Classification: 35J20, 35J60.

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