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.
Citation
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. https://doi.org/10.57262/die/1356060247
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