The Nonlinear Schrdinger Equations with Combined Nonlinearities of Power-Type and Hartree-Type

被引：2

作者：

Daoyuan FANG Zheng HAN Jialing DAI Department of MathematicsZhejiang UniversityHangzhou ChinaDepartment of MathematicsThe University of the PacificStocktonCA USA ^{[1
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机构：

来源：

ChineseAnnalsofMathematics(SeriesB) | 2011年 / 32卷 / 03期

关键词：

Global well-posedness; Scattering; blowup; Morawetz estimates; Perturbation principles;

D O I：

暂无

中图分类号：

O175.29 [非线性偏微分方程];

学科分类号：

070104 ;

摘要：

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 Hartreetype.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.

引用

页码：435 / 474

页数：40

共 29 条

[1]

The focusing energy-critical nonlinear Schrdinger equation in five and high. Killip,R,Visan,M. American Journal of Mathematics . 2010

[2]

Perturbation theory for linear operators. Kato,T. . 1980

[3]

Asymptotically linear solutions in H1of the2D defocusing nonlinear Schrdinger and Hartree equations. Holmer,J,Tzirakis,N. J.Hyperbolic Diff.Equ . 2010

[4]

On the blowing up of solutions to the Cauchy problem for nonlinear Schro¨dinger equations. Glassey R T. Journal of Mathematics . 1977

[5]

Global well-posedness, scattering and blow-up for the energycritical, focusing, non-linear Schr?dinger equation in the radial case. CE Kenig,F Merle. Inventiones Mathematicae . 2006

[6]

Minimal-mass blowup solutions of the mass-critical NLS. Tao,T,Visan,M,Zhang,X.Y. Forum Mathematicum . 2008

[7]

Stability of energy-critical nonlinear Schrdinger equations in high dimensions. Tao,T,Visan,M. Electron.J.Diff.Eqns . 2005

[8]

Global well-posedness and scattering for the defocusing energy-critical non-linear Schrdinger equation in R1+4. Ryckman,E,Visan,M. American Journal of Mathematics . 2007

[9]

Best constant in Sobolev inequality[J] . Giorgio Talenti. &nbspAnnali di Matematica Pura ed Applicata, Series 4 . 1976 (1)

[10]

Best constant in Sobolev inequality[J] . Giorgio Talenti. &nbspAnnali di Matematica Pura ed Applicata, Series 4 . 1976 (1)

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