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.

Keywords: contraction map, electromagnetic fields, multi-bump solutions, nonlinear Schrödinger equation, variational reduction method

@article{COCV_2013__19_1_91_0, author = {Pi, Huirong and Wang, Chunhua}, title = {Multi-bump solutions for nonlinear {Schr\"odinger} equations with electromagnetic fields}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {91--111}, publisher = {EDP-Sciences}, volume = {19}, number = {1}, year = {2013}, doi = {10.1051/cocv/2011207}, mrnumber = {3023062}, zbl = {1260.35212}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2011207/} }

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 SP - 91 EP - 111 VL - 19 IS - 1 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2011207/ DO - 10.1051/cocv/2011207 LA - en ID - COCV_2013__19_1_91_0 ER -

%0 Journal Article %A Pi, Huirong %A Wang, Chunhua %T Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields %J ESAIM: Control, Optimisation and Calculus of Variations %D 2013 %P 91-111 %V 19 %N 1 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2011207/ %R 10.1051/cocv/2011207 %G en %F COCV_2013__19_1_91_0

Pi, Huirong; Wang, Chunhua. Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields. ESAIM: Control, Optimisation and Calculus of Variations, Volume 19 (2013) no. 1, pp. 91-111. doi : 10.1051/cocv/2011207. http://archive.numdam.org/articles/10.1051/cocv/2011207/

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