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Global existence results for nonlinear Schrödinger equations with quadratic potentials
1.  MAB, UMR CNRS 5466 and Université Bordeaux 1, 351 cours de la Libération, F33 405 Talence cedex, France 
[1] 
Benjamin Dodson. Global wellposedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ via a linearnonlinear decomposition. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 19051926. doi: 10.3934/dcds.2013.33.1905 
[2] 
Takafumi Akahori. Low regularity global wellposedness for the nonlinear Schrödinger equation on closed manifolds. Communications on Pure and Applied Analysis, 2010, 9 (2) : 261280. doi: 10.3934/cpaa.2010.9.261 
[3] 
Daniela De Silva, Nataša Pavlović, Gigliola Staffilani, Nikolaos Tzirakis. Global wellposedness for a periodic nonlinear Schrödinger equation in 1D and 2D. Discrete and Continuous Dynamical Systems, 2007, 19 (1) : 3765. doi: 10.3934/dcds.2007.19.37 
[4] 
Zihua Guo, Yifei Wu. Global wellposedness for the derivative nonlinear Schrödinger equation in $H^{\frac 12} (\mathbb{R} )$. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 257264. doi: 10.3934/dcds.2017010 
[5] 
Daniela De Silva, Nataša Pavlović, Gigliola Staffilani, Nikolaos Tzirakis. Global wellposedness for the $L^2$ critical nonlinear Schrödinger equation in higher dimensions. Communications on Pure and Applied Analysis, 2007, 6 (4) : 10231041. doi: 10.3934/cpaa.2007.6.1023 
[6] 
Chao Yang. Sharp condition of global wellposedness for inhomogeneous nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems  S, 2021, 14 (12) : 46314642. doi: 10.3934/dcdss.2021136 
[7] 
Lassaad Aloui, Slim Tayachi. Local wellposedness for the inhomogeneous nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems, 2021, 41 (11) : 54095437. doi: 10.3934/dcds.2021082 
[8] 
Hiroyuki Hirayama, Mamoru Okamoto. Wellposedness and scattering for fourth order nonlinear Schrödinger type equations at the scaling critical regularity. Communications on Pure and Applied Analysis, 2016, 15 (3) : 831851. doi: 10.3934/cpaa.2016.15.831 
[9] 
Hiroyuki Hirayama. Wellposedness and scattering for a system of quadratic derivative nonlinear Schrödinger equations with low regularity initial data. Communications on Pure and Applied Analysis, 2014, 13 (4) : 15631591. doi: 10.3934/cpaa.2014.13.1563 
[10] 
Changxing Miao, Bo Zhang. Global wellposedness of the Cauchy problem for nonlinear Schrödingertype equations. Discrete and Continuous Dynamical Systems, 2007, 17 (1) : 181200. doi: 10.3934/dcds.2007.17.181 
[11] 
Yonggeun Cho, Gyeongha Hwang, Tohru Ozawa. Global wellposedness of critical nonlinear Schrödinger equations below $L^2$. Discrete and Continuous Dynamical Systems, 2013, 33 (4) : 13891405. doi: 10.3934/dcds.2013.33.1389 
[12] 
Yuanyuan Ren, Yongsheng Li, Wei Yan. Sharp wellposedness of the Cauchy problem for the fourth order nonlinear Schrödinger equation. Communications on Pure and Applied Analysis, 2018, 17 (2) : 487504. doi: 10.3934/cpaa.2018027 
[13] 
Junichi Segata. Wellposedness and existence of standing waves for the fourth order nonlinear Schrödinger type equation. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 10931105. doi: 10.3934/dcds.2010.27.1093 
[14] 
Kelin Li, Huafei Di. On the wellposedness and stability for the fourthorder Schrödinger equation with nonlinear derivative term. Discrete and Continuous Dynamical Systems  S, 2021, 14 (12) : 42934320. doi: 10.3934/dcdss.2021122 
[15] 
Boling Guo, Jun Wu. Wellposedness of the initialboundary value problem for the fourthorder nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems  B, 2022, 27 (7) : 37493778. doi: 10.3934/dcdsb.2021205 
[16] 
Massimo Cicognani, Michael Reissig. Wellposedness for degenerate Schrödinger equations. Evolution Equations and Control Theory, 2014, 3 (1) : 1533. doi: 10.3934/eect.2014.3.15 
[17] 
Shaoming Guo, Xianfeng Ren, Baoxiang Wang. Local wellposedness for the derivative nonlinear Schrödinger equation with $ L^2 $subcritical data. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 42074253. doi: 10.3934/dcds.2021034 
[18] 
Tarek Saanouni. Global wellposedness of some highorder semilinear wave and Schrödinger type equations with exponential nonlinearity. Communications on Pure and Applied Analysis, 2014, 13 (1) : 273291. doi: 10.3934/cpaa.2014.13.273 
[19] 
Ademir Pastor. On threewave interaction Schrödinger systems with quadratic nonlinearities: Global wellposedness and standing waves. Communications on Pure and Applied Analysis, 2019, 18 (5) : 22172242. doi: 10.3934/cpaa.2019100 
[20] 
DanAndrei Geba, Kenji Nakanishi, Sarada G. Rajeev. Global wellposedness and scattering for Skyrme wave maps. Communications on Pure and Applied Analysis, 2012, 11 (5) : 19231933. doi: 10.3934/cpaa.2012.11.1923 
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