| Issue |
ESAIM: COCV
Volume 19, Number 1, January-March 2013
|
|
|---|---|---|
| Page(s) | 91 - 111 | |
| DOI | https://doi.org/10.1051/cocv/2011207 | |
| Published online | 01 March 2012 | |
Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields
School of Mathematics and Statistics, Central China Normal
University, Wuhan
430079, P.R.
China
wch5923@yahoo.com.cn
Received:
2
May
2011
Revised:
30
November
2011
In this paper, we are concerned with the existence of multi-bump solutions for a nonlinear Schrödinger equations with electromagnetic fields. We prove under some suitable conditions that for any positive integer m, there exists ε(m) > 0 such that, for 0 < ε < ε(m), the problem has an m-bump complex-valued solution. As a result, when ε → 0, the equation has more and more multi-bump complex-valued solutions.
Mathematics Subject Classification: 35J10 / 35B99 / 35J60
Key words: Contraction map / electromagnetic fields / multi-bump solutions / nonlinear Schrödinger equation / variational reduction method
© EDP Sciences, SMAI, 2012
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