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Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity

Liu, Yue and Wang, Xiao-Ping and Wang, Ke (2006) Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity. Transactions of the American Mathematical Society, 358 (5). pp. 2105-2122. ISSN 0002-9947. https://resolver.caltech.edu/CaltechAUTHORS:20110721-080107918

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Abstract

This paper is concerned with the inhomogeneous nonlinear Shrödinger equation (INLS-equation)iu_t + Δu + V(Єx)│u│^pu = 0, x Є R^N. In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H^1(R^N) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small Є > 0.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1090/S0002-9947-05-03763-3DOIUNSPECIFIED
http://www.ams.org/journals/tran/2006-358-05/S0002-9947-05-03763-3/home.htmlPublisherUNSPECIFIED
Additional Information:© 2005 American Mathematical Society. Received by the editors April 16, 2003 and, in revised form, April 29, 2004. Article electronically published on May 9, 2005. The authors thank the referee for the careful reading of the manuscript and the valuable comments. This work is supported in part by RGC Competitive Earmarked Research Grant HKUST 6176/99P and HKUST 6143/01P.
Funders:
Funding AgencyGrant Number
RGC Competitive Earmarked ResearchHKUST 6176/99P
RGC Competitive Earmarked ResearchHKUST 6143/01P
Subject Keywords:Nonlinear Schrödinger equation, inhomogeneous nonlinearities, blow-up, standing waves, ground state, stability theory
Issue or Number:5
Classification Code:MSC (2000): Primary 35B35, 35B60, 35Q35, 35Q40, 35Q55, 76B25, 76E25, 76E30, 78A15
Record Number:CaltechAUTHORS:20110721-080107918
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110721-080107918
Official Citation:Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity Yue Liu; Xiao-Ping Wang; Ke Wang Trans. Amer. Math. Soc. 358 (2006), 2105-2122.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24486
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:21 Jul 2011 17:57
Last Modified:03 Oct 2019 02:56

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