关键词: Schrodinger方程, Dirichlet问题, 位势井, 整体W^1,2解

Abstract:

The global existence of Dirichlet problem for twoorder nonlinear Schrodinger 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., 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 W^1,2 solutions exist in potential well.

Key words: Schrodinger equations, Dirichlet problem, potential well, global W^1,2 solution