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...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.展开更多
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)+1 种基金the Science and Technology Foundation of Education Offce of Heilongjiang Province (No. 11541276)the Foundational Science Foundation of Harbin Engineering University
文摘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.
