一类具非线性二阶导数项的Schr dinger方程整体解存在的最佳条件

Sharp Condition of Global Existence for a Class of Second Order Derivative Nonlinear Schr dinger Equations

本文讨论一类具非线性二阶导数项的Schr(?)dinger方程,它在物理上描述了上混合振荡传播．根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在．

This paper discusses a type of second order derivative nonlinear SchrSdinger equations which are used to describe the upper-hybrid oscillation propagation in physics. In terms of the variational characteristics of the ground state, by applying the potential well argument and the concavity method, we get a sharp condition for global existence to the solutions of this equation. In addition, that how small the initial are, the global solutions exist is also given.