Well-posedness of Cauchy problem of fourth-order Schrödinger equations in anisotropic Sobolev space

Applied Mathematics and Computation ◽

10.1016/j.amc.2007.01.072 ◽

2007 ◽

Vol 190 (1) ◽

pp. 583-589 ◽

Author(s):

Cuihua Guo ◽

Shangbin Cui

Keyword(s):

Cauchy Problem ◽

Sobolev Space ◽

Fourth Order ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Anisotropic Sobolev Space

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Cauchy problem for higher-order Schrödinger equations in anisotropic Sobolev space

Applicable Analysis ◽

10.1080/00036810903277127 ◽

2009 ◽

Vol 88 (9) ◽

pp. 1329-1338 ◽

Author(s):

Cuihua Guo ◽

Xiangqing Zhao ◽

Xuemei Wei

Keyword(s):

Cauchy Problem ◽

Sobolev Space ◽

Higher Order ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Anisotropic Sobolev Space

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Well-posedness of Cauchy problem for the fourth order nonlinear Schrödinger equations in multi-dimensional spaces

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2006.05.031 ◽

2007 ◽

Vol 328 (1) ◽

pp. 58-83 ◽

Author(s):

Chengchun Hao ◽

Ling Hsiao ◽

Baoxiang Wang

Keyword(s):

Cauchy Problem ◽

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Well-posedness of the Cauchy problem of high dimension non-isotropic fourth-order Schrödinger equations in Sobolev spaces

Nonlinear Analysis ◽

10.1016/j.na.2008.07.032 ◽

2009 ◽

Vol 70 (10) ◽

pp. 3761-3772 ◽

Author(s):

Cuihua Guo ◽

Shangbin Cui

Keyword(s):

Cauchy Problem ◽

High Dimension ◽

Fourth Order ◽

Sobolev Spaces ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

The Cauchy Problem

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Global existence and asymptotic behavior of the Cauchy problem for fourth-order Schrödinger equations with combined power-type nonlinearities

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2012.03.028 ◽

2012 ◽

Vol 392 (2) ◽

pp. 111-122 ◽

Author(s):

Cuihua Guo

Keyword(s):

Cauchy Problem ◽

Asymptotic Behavior ◽

Global Existence ◽

Fourth Order ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

The Cauchy Problem

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Global well-posedness and scattering for the defocusing energy-critical nonlinear Schrödinger equations of fourth order in dimensions d⩾9

Journal of Differential Equations ◽

10.1016/j.jde.2011.08.009 ◽

2011 ◽

Vol 251 (12) ◽

pp. 3381-3402 ◽

Author(s):

Changxing Miao ◽

Guixiang Xu ◽

Lifeng Zhao

Keyword(s):

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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Global well-posedness and scattering for the fourth order nonlinear Schrödinger equations with small data in modulation and Sobolev spaces

Journal de Mathématiques Pures et Appliquées ◽

10.1016/j.matpur.2015.09.005 ◽

2016 ◽

Vol 105 (1) ◽

pp. 31-65 ◽

Author(s):

Michael Ruzhansky ◽

Baoxiang Wang ◽

Hua Zhang

Keyword(s):

Fourth Order ◽

Sobolev Spaces ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations

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On the well-posedness for stochastic fourth-order Schrödinger equations

Applied Mathematics-A Journal of Chinese Universities ◽

10.1007/s11766-011-2740-4 ◽

2011 ◽

Vol 26 (3) ◽

pp. 307-318 ◽

Author(s):

Dao-yuan Fang ◽

Lin-zi Zhang ◽

Ting Zhang

Keyword(s):

Fourth Order ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations

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On the Cauchy problem of fourth-order nonlinear Schrödinger equations

Nonlinear Analysis ◽

10.1016/j.na.2006.04.020 ◽

2007 ◽

Vol 66 (12) ◽

pp. 2911-2930 ◽

Author(s):

Ai Guo ◽

Shangbin Cui

Keyword(s):

Cauchy Problem ◽

Fourth Order ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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Global well-posedness for energy critical fourth-order Schrödinger equations in the radial case

Dynamics of Partial Differential Equations ◽

10.4310/dpde.2007.v4.n3.a1 ◽

2007 ◽

Vol 4 (3) ◽

pp. 197-225 ◽

Author(s):

Benoit Pausader

Keyword(s):

Fourth Order ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations ◽

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Multilinear estimates and well-posedness for the vortex filament fourth-order Schrödinger equations

Mathematical Methods in the Applied Sciences ◽

10.1002/mma.2684 ◽

2012 ◽

Vol 36 (11) ◽

pp. 1321-1333 ◽

Author(s):

Junyong Zhang ◽

Jiqiang Zheng

Keyword(s):

Fourth Order ◽

Vortex Filament ◽

Schrodinger Equations ◽

Well Posedness ◽

Schrödinger Equations

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