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Multi-bump solutions for nonlinear Schrödinger equations withelectromagnetic fields

Published online by Cambridge University Press:  01 March 2012

Huirong Pi  and
Chunhua Wang
Huirong Pi
Affiliation:
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P.R. China. wch5923@yahoo.com.cn
Chunhua Wang
Affiliation:
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P.R. China. wch5923@yahoo.com.cn
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Abstract

In this paper, we are concerned with the existence of multi-bump solutions for anonlinear Schrödinger equations with electromagnetic fields. We prove under some suitableconditions that for any positive integer m, there existsε(m) > 0 such that, for0 < ε < ε(m),the problem has an m-bump complex-valued solution. As a result, whenε → 0, the equation has more and more multi-bumpcomplex-valued solutions.

Keywords

Contraction mapelectromagnetic fieldsmulti-bump solutionsnonlinear Schrödinger equationvariational reduction method

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Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 19 , Issue 1 , January 2013 , pp. 91 - 111
Copyright
© EDP Sciences, SMAI, 2012

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