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Multi-bump solutions for nonlinear Schrödinger equations with electromagnetic fields

Huirong PiChunhua Wang — 2013

ESAIM: Control, Optimisation and Calculus of Variations

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 , there exists () > 0 such that, for 0 <  < (), the problem has an -bump complex-valued solution. As a result, when  → 0, the equation has more and more multi-bump complex-valued solutions.

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