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| The Nonlinear Schr¨odinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type |
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Citation： |
Daoyuan FANG,Zheng HAN,Jialing DAI.The Nonlinear Schr¨odinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type[J].Chinese Annals of Mathematics B,2011,32(3):435~474 |
| Page view： 1818
Net amount： 1401 |
Authors： |
Daoyuan FANG; Zheng HAN; Jialing DAI; |
Foundation： |
the National Natural Science Foundation of China (Nos. 10871175, 10931007)
and the Zhejiang Provincial Natural Science Foundation of China (No. Z6100217). |
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| Abstract： |
The primary goal of this paper is to present a comprehensive study of the nonlinear
Schr¨odinger equations with combined nonlinearities of the power-type and Hartreetype.
Under certain structural conditions, the authors are able to provide a complete
picture of how the nonlinear Schr¨odinger 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 |
Classification： |
35M10 |
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