Articles

ON THE CONCENTRATION PROPERTIES FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A STARK POTENTIAL

  • ZHU Shi-Hui ,
  • ZHANG Jian
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Received date: 2009-12-01

  Online published: 2011-09-20

Supported by

This work supported by National Science Foundation of China (11071177). †Corresponding author: Zhu Shihui.

Abstract

In this paper, we study blow-up solutions of the Cauchy problem to the L2 critical nonlinear Schr¨odinger equation with a Stark potential. Using the variational char-acterization of the ground state for nonlinear Schr¨odinger equation without any potential, we obtain some concentration properties of blow-up solutions, including that the origin is the blow-up point of the radial blow-up solutions, the phenomenon of L2-concentration and rate of L2-concentration of blow-up solutions.

Cite this article

ZHU Shi-Hui , ZHANG Jian . ON THE CONCENTRATION PROPERTIES FOR THE NONLINEAR SCHRÖDINGER EQUATION WITH A STARK POTENTIAL[J]. Acta mathematica scientia, Series B, 2011 , 31(5) : 1923 -1938 . DOI: 10.1016/S0252-9602(11)60371-8

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