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ESAIM: Control, Optimisation and Calculus of Variations (1)

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Multi-bump solutions for nonlinear Schrödinger equations withelectromagnetic fields
Huirong Pi, Chunhua Wang
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 19 / Issue 1 / January 2013

Published online by Cambridge University Press:

01 March 2012, pp. 91-111

Print publication:

January 2013
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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.