Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields
School of Mathematics and Statistics, Central China Normal
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