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Abstract and Applied Analysis
Volume 2013, Article ID 238410, 14 pages
http://dx.doi.org/10.1155/2013/238410
Research Article

Phenomena of Blowup and Global Existence of the Solution to a Nonlinear Schrödinger Equation

1School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China
2Department of Basic Curriculum, The Chinese People’s Armed Police Force Academy, Lang Fang, He Bei 065000, China
3Department of Mathematics, School of Science, Tianjin University, Tianjin 300072, China

Received 26 August 2013; Accepted 13 October 2013

Academic Editor: Sining Zheng

Copyright © 2013 Xiaowei An et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the following Cauchy problem: where and are real-valued potentials and and is even, is measurable in and continuous in , and is a complex-valued function of . We obtain some sufficient conditions and establish two sharp thresholds for the blowup and global existence of the solution to the problem.