一类带调和势的非线性Schrdinger方程解的性质

The Blow-up of Solutions to a Class of Nonlinear Schrdinger Equation with Harmonic Potentials

研究一类带调和势的非线性Schrdinger方程的初值问题:itφ=-12Δφ+12|x|pφ-a|φ|2φ-b|φ4|φ,(t 0,x∈R,p>0,a,b为常数)应用能量方法得到了只要初值满足一定条件,方程的解就会在有限的时间内发生爆破.

The research studies a Class of Nonlinear Schrodinger Equation with Harmonic Potential iφt=-12Δφ＋12｜x｜pφ-a｜φ｜2φ-b｜φ4｜φ,（t 0,x∈R,p〉0,a,b为常数） By using energy method, it has been proved that if the initial data is satisfied with some conditions,the solutions of equation will blow-up in finite time T〈∞.