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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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