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January  2008, 7(1): 83-88. doi: 10.3934/cpaa.2008.7.83

A variational argument to finding global solutions of a quasilinear Schrödinger equation

Jianqing Chen 1,

1. 

Department of Mathematics, Fujian Normal University, Fuzhou, 350007

Received  November 2006 Revised  June 2007 Published  October 2007

We prove a sharp existence result of global solutions of the quasilinear Schrödinger equation

$iu_t + u_{x x} + |u|^{p-2}u +(|u|^2)_{x x}u = 0,\quad u|_{t=0}=u_0(x),\quad x\in \mathbb R$

for a large class of initial data. The result gives a qualitative description on how small an initial data can ensure the existence of global solutions which sharpen a global existence result with small initial data [7, 10].

Keywords: Global solutions, quasilinear Schrödinger equation..
Mathematics Subject Classification: Primary: 35J20; Secondary: 35Q5.
Citation: Jianqing Chen. A variational argument to finding global solutions of a quasilinear Schrödinger equation. Communications on Pure & Applied Analysis, 2008, 7 (1) : 83-88. doi: 10.3934/cpaa.2008.7.83
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