Geodesic
Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 91-111.

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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.

DOI : 10.1051/cocv/2011207
Classification : 35J10, 35B99, 35J60
Keywords: contraction map, electromagnetic fields, multi-bump solutions, nonlinear Schrödinger equation, variational reduction method 
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     title = {Multi-bump solutions for nonlinear {Schr\"odinger} equations with electromagnetic fields},
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Pi, Huirong; Wang, Chunhua. Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 91-111. doi : 10.1051/cocv/2011207. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011207/

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