Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields

Huirong Pi; Chunhua Wang

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 1, page 91-111
  • ISSN: 1292-8119

Abstract

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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.

How to cite

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Pi, Huirong, and Wang, Chunhua. "Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 91-111. <http://eudml.org/doc/272822>.

@article{Pi2013,
abstract = {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) &gt; 0 such that, for 0 &lt; ε &lt; 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.},
author = {Pi, Huirong, Wang, Chunhua},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {contraction map; electromagnetic fields; multi-bump solutions; nonlinear Schrödinger equation; variational reduction method},
language = {eng},
number = {1},
pages = {91-111},
publisher = {EDP-Sciences},
title = {Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields},
url = {http://eudml.org/doc/272822},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Pi, Huirong
AU - Wang, Chunhua
TI - Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 1
SP - 91
EP - 111
AB - 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) &gt; 0 such that, for 0 &lt; ε &lt; 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.
LA - eng
KW - contraction map; electromagnetic fields; multi-bump solutions; nonlinear Schrödinger equation; variational reduction method
UR - http://eudml.org/doc/272822
ER -

References

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