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2004 On the critical exponent for the Schrödinger equation with a nonlinear boundary condition
Azmy S. Ackleh, Keng Deng
Differential Integral Equations 17(11-12): 1293-1307 (2004).

Abstract

We study the Schrödinger equation: $iu_t+u_{xx}=0,$ $ x\in {\bf R}_+,$ $ t>0$ with a nonlinear boundary condition $-u_x(0,t)=\vert u(0,t)\vert ^{p-1} u(0,t),$ $ t>0$. We show that if $1 <p <3,$ every solution is global in $H^1({\bf R}_+)$, while if $p\ge 3$, then nonglobal solutions exist.

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Azmy S. Ackleh. Keng Deng. "On the critical exponent for the Schrödinger equation with a nonlinear boundary condition." Differential Integral Equations 17 (11-12) 1293 - 1307, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1150.35303
MathSciNet: MR2100028

Subjects:
Primary: 35J65
Secondary: 35B33 , 35J05

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 11-12 • 2004
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