中文摘要：

利用位势井方法研究有界域上二阶非线性Schrdinger方程Dirichlet问题整体解的存在性,得到了位势井深度d=（1/γCγ＊）〉0,其中：γ=（2（p＋1））/（p-1）;C＊=sup（（‖u‖p＋1）/‖▽u‖）,明确了位势井的形态.通过构造问题近似解得到了近似解的先验估计及相关集合在流之下的不变性,揭示了满足适当条件时在位势井内整体W1,2解的存在性.

英文摘要：

The global existence of Dirichlet problem for two-order nonlinear Schrdinger equations was studied.By means of the potential well method combined with embedding theorem in Sobolev space,the value of the depth of potential well was obtained,i.e.,d=（1/γCγ＊）＆gt;0,where γ=（2（p＋1））/（p-1）;C＊=sup（（‖u‖p＋1）/‖▽u‖）.Then the function space was pointed out in which the solutions exist by constructing and estimating the norm of the approximate solutions of the problem.It was shown that the global W1,2 solutions exist in potential well.