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Stable standing waves for a class of nonlinear Schrödinger-Poisson equations

Bellazzini, Jacopo and Siciliano, Gaetano (2011) Stable standing waves for a class of nonlinear Schrödinger-Poisson equations. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 62 (2), p. 267-280. eISSN 1420-9039. Article.

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DOI: 10.1007/s00033-010-0092-1


We prove the existence of orbitally stable standing waves with prescribed L 2-norm for the following Schrödinger-Poisson type equation
when p ε {8/3} U(3, 10/3). In the case 3 < p < 10/3, we prove the existence and stability only for sufficiently large L 2-norm. In case p=8/3, our approach recovers the result of Sanchez and Soler (J. Stat. Phys. 114:179–204, 2004) for sufficiently small charges. The main point is the analysis of the compactness of minimizing sequences for the related constrained minimization problem. In the final section, a further application to the Schrödinger equation involving the biharmonic operator is given.

Item Type:Article
ID Code:6677
Uncontrolled Keywords:Schrödinger-Poisson equations, standing waves, orbital stability
Subjects:Area 01 - Scienze matematiche e informatiche > MAT/05 Analisi matematica
Divisions:001 Università di Sassari > 01 Dipartimenti > Scienze botaniche, ecologiche e geologiche
Copyright Holders:© 2010 Springer Basel AG
Deposited On:07 Dec 2011 12:44

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