期刊论文、会议论文

Long, Wei（彭双阶）

英文

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

1078-0947

2016

36

2

917-939

Xiamen Univ, Xiamen, PEOPLES R CHINA

Xiamen Univ

PO BOX 2604, SPRINGFIELD, MO 65801-2604 USA

AMER INST MATHEMATICAL SCIENCES-AIMS

10.3934/dcds.2016.36.917

The authors wish to thank all the colleagues that have given permission to reproduce figures from their articles. Also they thank Dr. R. Dmowska, Harvard University, who encouraged us to write this chapter, and Drs. J. Mezcua, Instituto Geográfico Nacional, Madrid, and A. F. Espinosa de los Monteros, U.S. Geological Survey, Denver, Colorado for their help. This work was partially supported by Dirección General de Investigatión Cientifica y Técnica, Spain, project PB92-0184 and the European Community DG XII, EPOCH, CT91-0042. Publication No. 354 of the Dpto. de Geofísica, Universidad Complutense, Madrid.

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We consider the following nonlinear fractional scalar field equation $$ (-\Delta)^s u + u = K(|x|)u^p,\ \ u > 0 \ \ \hbox{in}\ \ \mathbb{R}^N, $$ where $K(|x|)$ is a positive radial function, $N\ge 2$, $0 < s < 1$, and $1 < p < \frac{N+2s}{N-2s}$. Under various asymptotic assumptions on $K(x)$ at infinity, we show that this problem has infinitely many non-radial positive solutions and sign-changing solu...