| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4610576 | Journal of Differential Equations | 2014 | 22 Pages |
Abstract
We study the following nonlinear Schrödinger equationiut=−Δu+V(x)u−a|u|qu,(t,x)∈R1×R2, where a>0a>0, q∈(0,2)q∈(0,2), and V(x)V(x) is some type of trapping potential. For any fixed a>a⁎:=‖Q‖22, where Q is the unique (up to translations) positive radial solution of Δu−u+u3=0Δu−u+u3=0 in R2R2, by directly using constrained variational method and energy estimates we present a detailed analysis of the concentration and symmetry breaking of standing waves for the above equation as q↗2q↗2.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yujin Guo, Xiaoyu Zeng, Huan-Song Zhou,