Notes on the Cauchy problem for the self-adjoint and non-self-adjoint Schrödinger equations with polynomially growing potentials

Journal of Pseudo-Differential Operators and Applications ◽

10.1007/s11868-019-00301-6 ◽

2019 ◽

Vol 11 (2) ◽

pp. 703-731 ◽

Author(s):

Wataru Ichinose ◽

Takayoshi Aoki

Keyword(s):

Cauchy Problem ◽

The Self ◽

Schrodinger Equations ◽

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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On the Cauchy problem for the nonlinear Schrödinger equations with time-dependent linear loss/gain

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2014.03.019 ◽

2014 ◽

Vol 416 (2) ◽

pp. 901-923 ◽

Author(s):

Binhua Feng ◽

Dun Zhao ◽

Chunyou Sun

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Time Dependent ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem ◽

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Nonlinear Schrödinger equations in inhomogeneous media: wellposedness and illposedness of the Cauchy problem

Proceedings of the International Congress of Mathematicians Madrid, August 22–30, 2006 ◽

10.4171/022-3/8 ◽

2009 ◽

pp. 156-182

Author(s):

Patrick Gérard

Keyword(s):

Cauchy Problem ◽

Inhomogeneous Media ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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The Cauchy problem for non-autonomous nonlinear Schrödinger equations

Science in China Series A Mathematics ◽

10.1360/04ys0012 ◽

2005 ◽

Vol 48 (4) ◽

pp. 522 ◽

Author(s):

Y. H. Pang Peter

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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Sharp weights in the Cauchy problem for nonlinear Schrödinger equations with potential

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-015-0501-6 ◽

2015 ◽

Vol 66 (4) ◽

pp. 2087-2094 ◽

Author(s):

Rémi Carles

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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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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Nonexistence of Global Solutions to the Cauchy Problem for the Damped Nonlinear Schrödinger Equations

SIAM Journal on Mathematical Analysis ◽

10.1137/0515028 ◽

1984 ◽

Vol 15 (2) ◽

pp. 357-366 ◽

Author(s):

Masayoshi Tsutsumi

Keyword(s):

Cauchy Problem ◽

Global Solutions ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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The Cauchy problem for nonlinear Schrödinger equations in modulation spaces

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2015.01.005 ◽

2015 ◽

Vol 24 ◽

pp. 83-97 ◽

Author(s):

Shaolei Ru ◽

Jiecheng Chen

Keyword(s):

Cauchy Problem ◽

Nonlinear Schrödinger Equations ◽

Modulation Spaces ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Nonlinear Schrodinger Equations ◽

The Cauchy Problem

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On the Cauchy problem of 3-D energy-critical Schrödinger equations with subcritical perturbations

Journal of Differential Equations ◽

10.1016/j.jde.2006.08.010 ◽

2006 ◽

Vol 230 (2) ◽

pp. 422-445 ◽

Author(s):

Xiaoyi Zhang

Keyword(s):

Cauchy Problem ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

The Cauchy Problem

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Global Small Solutions of the Cauchy Problem for Nonisotropic Schrödinger Equations

Kyungpook mathematical journal ◽

10.5666/kmj.2008.48.1.101 ◽

2008 ◽

Vol 48 (1) ◽

pp. 101-108 ◽

Author(s):

Xiangqing Zhao ◽

Shangbin Cui

Keyword(s):

Cauchy Problem ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

The Cauchy Problem

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