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| The Nonlinear Schr¨odinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type | |
| 引用本文： | Daoyuan FANG,Zheng HAN,Jialing DAI. The Nonlinear Schr¨odinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type[J]. 数学年刊B辑(英文版), 2011, 32(3): 435-474. DOI: 10.1007/s11401-011-0642-7 |
| 作者姓名： | Daoyuan FANG Zheng HAN Jialing DAI |
| 基金项目： | Project supported by the National Natural Science Foundation of China （Nos. 10871175, 10931007） and the Zhejiang Provincial Natural Science Foundation of China （No. Z6100217）. |
| 摘 要： | |
| 关 键 词： | 非线性方程 非线性薛定谔方程 ee型 功率型 结构条件 能量空间 |
The Nonlinear SchrSdinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type |
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| Daoyuan FANG,Zheng HAN and Jialing DAI. The Nonlinear SchrSdinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type[J]. Chinese Annals of Mathematics,Series B, 2011, 32(3): 435-474. DOI: 10.1007/s11401-011-0642-7 | |
| Authors: | Daoyuan FANG Zheng HAN Jialing DAI |
| Affiliation: | 1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China 2. Department of Mathematics, The University of the Pacific, Stockton, CA, 95211, USA |
| Abstract: | The primary goal of this paper is to present a comprehensive study of the nonlinear Schr?dinger equations with combined nonlinearities of the power-type and Hartree-type. Under certain structural conditions, the authors are able to provide a complete picture of how the nonlinear Schr?dinger equations with combined nonlinearities interact in the given energy space. The method used in the paper is based upon the Morawetz estimates and perturbation principles. |
| Keywords: | Global well-posedness Scattering blowup Morawetz estimates Perturbation principles |
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