一类带调和势具非齐次项的非线性Schrdinger方程  

Inhomogeneous Nonlinear Schrdinger Equation with Harmonic Potential

作　　者：佘朝兵[1,2] 何小飞[1,2] 谌凤霞 

机构地区：[1]吉首大学数学与统计学院,湖南吉首416000 [2]吉首大学张家界学院,湖南张家界427000

出　　处：《吉首大学学报（自然科学版）》2016年第3期4-9,13,共7页Journal of Jishou University(Natural Sciences Edition)

基　　金：吉首大学张家界学院科研资助项目(ZYYB201605)

摘　　要：讨论一类带调和势的具有非齐次项的非线性Schrdinger方程初值问题.通过构造对应的能量泛函、变分结构,运用势井方法、凹函数和改进过的Gagliardo-Nirenberg插值不等式,得到Cauchy问题整体解及爆破解存在的最佳条件,并且证明了整体解存在的初值具体取值范围.The inhomogeneous nonlinear Schrdinger equation with harmonic potential is discussed.By establishing the corresponding energy function and the variational structure and through applying the potential well argument,the concave function and the improved Gagliardo-Nirenberg interpolation inequation,the optimum conditions for the global solution and explosive solution for the Cauchy problem are obtained.In addition,the initial value for the existence of global solution is determined.

关 键 词：非齐次项 非线性Schrdinger方程 整体解 爆破解 最佳条件 

分 类 号：O241.8[理学—计算数学]