二阶非线性Schr odinger方程Dirichlet问题的整体W^(1,2)解  

Global W^(1,2) Solution of Dirichlet Problem for Two-Order Nonlinear Schrodinger Equation

作　　者：宋玉坤[1,2] 陈阳[2] 袁洪君[1] 

机构地区：[1]吉林大学数学研究所,长春130012 [2]承德石油高等专科学校数理部,河北承德067000

出　　处：《吉林大学学报（理学版）》2013年第2期179-182,共4页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:10971080);河北省高等学校自然科学研究项目(批准号:z2010209)

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.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.

关 键 词：SCHRODINGER方程 DIRICHLET问题 位势井 整体W^(1 2)解 

分 类 号：O175.26[理学—数学]