Multi-bump solutions for the nonlinear Schrödinger-Poisson system.(English)Zbl 1317.35238

Summary: In this paper, we study a kind of nonlinear Schrödinger-Poisson system with a parameter $$\epsilon$$. For any positive integer $$m$$, we prove that there exists $$\epsilon(m) > 0$$ such that, for $$0 < \epsilon < \epsilon(m)$$, the equation has an $$m$$-bump positive solution under some suitable conditions. As a consequence, the equation has more and more multi-bump positive solutions as $$\epsilon \to 0$$.{
©2011 American Institute of Physics}

MSC:

 35Q55 NLS equations (nonlinear Schrödinger equations) 35B09 Positive solutions to PDEs 82D37 Statistical mechanics of semiconductors
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References:

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