Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity
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- by Yue Liu, Xiao-Ping Wang and Ke Wang PDF
- Trans. Amer. Math. Soc. 358 (2006), 2105-2122 Request permission
Abstract:
This paper is concerned with the inhomogeneous nonlinear Shrödinger equation (INLS-equation) \begin{equation*}i u_t + \Delta u + V(\epsilon x) |u|^p u = 0, \; x \in {\mathbf R}^N. \end{equation*} In the critical and supercritical cases $p \ge 4/N,$ with $N \ge 2,$ it is shown here that standing-wave solutions of (INLS-equation) on $H^1({\mathbf R}^N)$ perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small $\epsilon > 0.$References
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Additional Information
- Yue Liu
- Affiliation: Department of Mathematics, University of Texas, Arlington, Texas 76019
- Email: yliu@uta.edu
- Xiao-Ping Wang
- Affiliation: Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
- Email: mawang@ust.hk
- Ke Wang
- Affiliation: California Institute of Technology, MC 217-50, 1200 E. California Boulevard, Pasadena, California 91125
- Email: wang@acm.caltech.edu
- Received by editor(s): April 16, 2003
- Received by editor(s) in revised form: April 29, 2004
- Published electronically: May 9, 2005
- © Copyright 2005 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 358 (2006), 2105-2122
- MSC (2000): Primary 35B35, 35B60, 35Q35, 35Q40, 35Q55, 76B25, 76E25, 76E30, 78A15
- DOI: https://doi.org/10.1090/S0002-9947-05-03763-3
- MathSciNet review: 2197450