Nonlinear Schrdinger equation with combined power-type nonlinearities and harmonic potential  

作　　者：徐润章 徐闯 

机构地区：[1]College of Science, Harbin Engineering University [2]Department of Mathematics, Harbin Institute of Technology

出　　处：《Applied Mathematics and Mechanics(English Edition)》2010年第4期521-528,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (Nos. 10871055 and 10926149);the Natural Science Foundation of Heilongjiang Province (Nos. A200702 and A200810);the Science and Technology Foundation of Education Offce of Heilongjiang Province (No. 11541276);the Foundational Science Foundation of Harbin Engineering University

摘　　要：This paper discusses a class of nonlinear SchrSdinger equations with combined power-type nonlinearities and harmonic potential. By constructing a variational problem the potential well method is applied. The structure of the potential well and the properties of the depth function are given. The invariance of some sets for the problem is shown. It is proven that, if the initial data are in the potential well or out of it, the solutions will lie in the potential well or lie out of it, respectively. By the convexity method, the sharp condition of the global well-posedness is given.This paper discusses a class of nonlinear SchrSdinger equations with combined power-type nonlinearities and harmonic potential. By constructing a variational problem the potential well method is applied. The structure of the potential well and the properties of the depth function are given. The invariance of some sets for the problem is shown. It is proven that, if the initial data are in the potential well or out of it, the solutions will lie in the potential well or lie out of it, respectively. By the convexity method, the sharp condition of the global well-posedness is given.

关 键 词：sharp criterion invariant manifold harmonic potential combined powertype nonlinearities 

分 类 号：O175.29[理学—数学] TN929.11[理学—基础数学]