On a Class of Quasilinear SchrLdinger Equations
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摘要: 在二维空间中讨论一类拟线性Schrdinger方程,该方程在物理学上描述了吸引玻色-爱因斯坦凝聚.通过建立这个方程的性质,运用能量方法,证明了该方程所对应的初值问题的解在一定条件下爆破.同时利用变分方法,也得到了整体解存在的一个充分条件,该条件与一个经典的椭圆方程的基态有关.
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关键词:
- 拟线性Schrdinger方程 /
- 爆破 /
- 整体解 /
- 基态 /
- 玻色-爱因斯坦凝聚
Abstract: A type of quasilinear SchrLdinger equations in two dimensions are discussed, which describe attractive Bose-Einstein Condensates in physics. By establishing the property of the equation and applying the energymethod, was proved the blowup of the solutions to the Cauchy problem for the equation under certain conditions. At the same time, by the variational method, the a sufficient condition of global existence was got, which is related to the ground state of a classical elliptic equation.-
Key words:
- quasilinear SchrLdinger equations /
- blow up /
- global solution /
- ground state /
- Bose-Einstein condensates
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