The initial value problem for cubic semilinear Schrodinger equations

被引：23

作者：

Chihara, H ^{[1
]}

机构：

[1] SHINSHU UNIV,DEPT MATH,MATSUMOTO,NAGANO 390,JAPAN

来源：

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES | 1996年 / 32卷 / 03期

关键词：

D O I：

10.2977/prims/1195162851

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present local and global existence theorems for cubic semilinear Schrodinger equations. Our new results are the improvement of our previous ones ([2],[3],[4]). The idea of the proof consists of the energy and the decay estimates. These equations do not allow the classical energy estimates. To avoid this difficulty, we make strong use of S. Doi's method for linear Schrodinger type equations. Combining cubic nonlinearity and S. Doi's method, we obtain the improved results.

引用

页码：445 / 471

页数：27

共 20 条

[1]

[Anonymous], 1981, PSEUDO DIFFERENTIAL

[2] Global existence of small solutions to semilinear Schrodinger equations with gauge invariance [J].