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July/August 2009 Orbital stability of standing waves of semiclassical nonlinear Schrödinger-Poisson equation
Isabella Ianni, Stefan Le Coz
Adv. Differential Equations 14(7/8): 717-748 (July/August 2009).

Abstract

We study the orbital stability of single-spike semiclassical standing waves of a nonhomogeneous in space nonlinear Schrödinger-Poisson equation. When the nonlinearity is subcritical or supercritical we prove that the nonlocal Poisson-term does not influence the stability of standing waves, whereas in the critical case it may create instability if its value at the concentration point of the spike is too large. The proofs are based on the study of the spectral properties of a linearized operator and on the analysis of a slope condition. Our main tools are perturbation methods and asymptotic expansion formulas.

Citation

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Isabella Ianni. Stefan Le Coz. "Orbital stability of standing waves of semiclassical nonlinear Schrödinger-Poisson equation." Adv. Differential Equations 14 (7/8) 717 - 748, July/August 2009.

Information

Published: July/August 2009
First available in Project Euclid: 18 December 2012

zbMATH: 1181.35262
MathSciNet: MR2527691

Subjects:
Primary: 35B35, 35Q51, 35Q55

Rights: Copyright © 2009 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.14 • No. 7/8 • July/August 2009
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