刘秀英

• 1:菏泽学院数学系

摘要(Abstract)：

研究一类带调和势的非线性Schrdinger方程iut=-Δu+|x|2u-k(x)|u|N4u的初值问题。运用能量方法得到了该方程初值问题的爆破性质。

关键词(KeyWords)： 非线性Schrdinger方程;爆破;调和势

Abstract:

Keywords:

基金项目(Foundation): 菏泽学院科学研究基金资助项目(XY07XY01)

作者(Author): 刘秀英

DOI: 10.16393/j.cnki.37-1436/z.2008.05.006

参考文献(References)：

• [1]Weinstein M I.Nonlinear schrdinger Equation and sharp interpolation estimate[J].Commun Math Phys,1983,87(4):567-576.
• [2]Zhang J.Sharp conditions of global existence for nonlinear schr dinger and Klein-Gordon equations[J].Nonlinear Analysis,2002,48(2):191-207.
• [3]Merle F.Nonexistence of minimal blow-up solutions of equations iut=-Δu-k(x)|u|4nuin Rn[J].Ann Inst Henri PoincarePhsique Theorique,1996,64(1):33-85.
• [4]舒级,张健.低维空间中的吸引玻色-爱因斯坦凝聚的坍塌性质[J].四川师范大学学报:自然科学版,2004,27(3):230-233.
• [5]Sulem C,Sulem P L.The Nonlinear schr dinger Equation,Self-focusing and Wave Collapse[M].New York:Springer,1999.
• [6]Zhang J.Stability of standing waves for nonlinear Schr dinger equations with unbounded potentials[J].Z Angew Math Phys,2000,51(3):498-503.
• [7]Zhang J.stability of attractive Bose-Einstien condensates[J].J Stat Phys,2000,101(3~4):731-746.
• [8]Cazenave T.An introduction to Nonlinear Schr dinger Equations[M].Rio de Janeiro:Textos de metodos mathmatics,1989.
• [9]Oh Y G.Cauchy problem and Ehrenfest's of nonlinear Schr dinger equations with potentials[J].J Diff Equa,1989,81:255-274.