Geodesic
Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential
Xing Cheng 1   ; Yanfang Gao 2
1 Department of Mathematics University of Science and Technology of China Hefei 230026, China
2 School of Mathematics and Computer Science Fujian Normal University Fuzhou, China, 350117
Colloquium Mathematicum, Tome 134 (2014) no. 1, pp. 143-149 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential \[ {\mathrm i}\partial_t u + \tfrac{1}{2}\varDelta u - \tfrac12 |x|^2 u = -|u|^{4/(d-2)}u, \quad x \in \mathbb R^d, \] is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.
DOI : 10.4064/cm134-1-7
Keywords: focusing nonlinear schr dinger equation nls confining harmonic potential mathrm partial tfrac vardelta tfrac d quad mathbb considered modifying variational technique shall sufficient condition under which corresponding solution blows

Xing Cheng  1   ; Yanfang Gao  2

1 Department of Mathematics University of Science and Technology of China Hefei 230026, China
2 School of Mathematics and Computer Science Fujian Normal University Fuzhou, China, 350117 
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     title = {Blow-up for the focusing energy critical
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Xing Cheng; Yanfang Gao. Blow-up for the focusing energy critical
 nonlinear Schrödinger equation with
 confining harmonic potential. Colloquium Mathematicum, Tome 134 (2014) no. 1, pp. 143-149. doi: 10.4064/cm134-1-7

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