Advances in Differential Equations

Orbital stability of standing waves of semiclassical nonlinear Schrödinger-Poisson equation

Isabella Ianni and Stefan Le Coz

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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.

Article information

Adv. Differential Equations, Volume 14, Number 7/8 (2009), 717-748.

First available in Project Euclid: 18 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35Q51: Soliton-like equations [See also 37K40] 35B35: Stability


Ianni, Isabella; Le Coz, Stefan. Orbital stability of standing waves of semiclassical nonlinear Schrödinger-Poisson equation. Adv. Differential Equations 14 (2009), no. 7/8, 717--748.

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