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Blowup and global existence of the nonlinear Schrödinger equations with multiple potentials
1. | College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068 |
2. | Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088 |
[1] |
Masahoto Ohta, Grozdena Todorova. Remarks on global existence and blowup for damped nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2009, 23 (4) : 1313-1325. doi: 10.3934/dcds.2009.23.1313 |
[2] |
Rémi Carles. Global existence results for nonlinear Schrödinger equations with quadratic potentials. Discrete and Continuous Dynamical Systems, 2005, 13 (2) : 385-398. doi: 10.3934/dcds.2005.13.385 |
[3] |
Congming Peng, Dun Zhao. Global existence and blowup on the energy space for the inhomogeneous fractional nonlinear Schrödinger equation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (7) : 3335-3356. doi: 10.3934/dcdsb.2018323 |
[4] |
Gan Lu, Weiming Liu. Multiple complex-valued solutions for the nonlinear Schrödinger equations involving magnetic potentials. Communications on Pure and Applied Analysis, 2017, 16 (6) : 1957-1975. doi: 10.3934/cpaa.2017096 |
[5] |
Eduard Toon, Pedro Ubilla. Existence of positive solutions of Schrödinger equations with vanishing potentials. Discrete and Continuous Dynamical Systems, 2020, 40 (10) : 5831-5843. doi: 10.3934/dcds.2020248 |
[6] |
Xing Cheng, Ze Li, Lifeng Zhao. Scattering of solutions to the nonlinear Schrödinger equations with regular potentials. Discrete and Continuous Dynamical Systems, 2017, 37 (6) : 2999-3023. doi: 10.3934/dcds.2017129 |
[7] |
Yongsheng Jiang, Huan-Song Zhou. A sharp decay estimate for nonlinear Schrödinger equations with vanishing potentials. Communications on Pure and Applied Analysis, 2010, 9 (6) : 1723-1730. doi: 10.3934/cpaa.2010.9.1723 |
[8] |
J. Colliander, Justin Holmer, Monica Visan, Xiaoyi Zhang. Global existence and scattering for rough solutions to generalized nonlinear Schrödinger equations on $R$. Communications on Pure and Applied Analysis, 2008, 7 (3) : 467-489. doi: 10.3934/cpaa.2008.7.467 |
[9] |
Tadahiro Oh. Global existence for the defocusing nonlinear Schrödinger equations with limit periodic initial data. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1563-1580. doi: 10.3934/cpaa.2015.14.1563 |
[10] |
Jason Murphy, Fabio Pusateri. Almost global existence for cubic nonlinear Schrödinger equations in one space dimension. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2077-2102. doi: 10.3934/dcds.2017089 |
[11] |
Zaihui Gan, Jian Zhang. Blow-up, global existence and standing waves for the magnetic nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2012, 32 (3) : 827-846. doi: 10.3934/dcds.2012.32.827 |
[12] |
Tai-Chia Lin, Tsung-Fang Wu. Multiple positive solutions of saturable nonlinear Schrödinger equations with intensity functions. Discrete and Continuous Dynamical Systems, 2020, 40 (4) : 2165-2187. doi: 10.3934/dcds.2020110 |
[13] |
Renata Bunoiu, Radu Precup, Csaba Varga. Multiple positive standing wave solutions for schrödinger equations with oscillating state-dependent potentials. Communications on Pure and Applied Analysis, 2017, 16 (3) : 953-972. doi: 10.3934/cpaa.2017046 |
[14] |
Xuan Liu, Ting Zhang. $ H^2 $ blowup result for a Schrödinger equation with nonlinear source term. Electronic Research Archive, 2020, 28 (2) : 777-794. doi: 10.3934/era.2020039 |
[15] |
Thierry Cazenave, Yvan Martel, Lifeng Zhao. Finite-time blowup for a Schrödinger equation with nonlinear source term. Discrete and Continuous Dynamical Systems, 2019, 39 (2) : 1171-1183. doi: 10.3934/dcds.2019050 |
[16] |
Jianqing Chen, Boling Guo. Sharp global existence and blowing up results for inhomogeneous Schrödinger equations. Discrete and Continuous Dynamical Systems - B, 2007, 8 (2) : 357-367. doi: 10.3934/dcdsb.2007.8.357 |
[17] |
Juan Belmonte-Beitia, Vladyslav Prytula. Existence of solitary waves in nonlinear equations of Schrödinger type. Discrete and Continuous Dynamical Systems - S, 2011, 4 (5) : 1007-1017. doi: 10.3934/dcdss.2011.4.1007 |
[18] |
Tai-Chia Lin, Tsung-Fang Wu. Existence and multiplicity of positive solutions for two coupled nonlinear Schrödinger equations. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2911-2938. doi: 10.3934/dcds.2013.33.2911 |
[19] |
Teresa D'Aprile. Some existence and concentration results for nonlinear Schrödinger equations. Communications on Pure and Applied Analysis, 2002, 1 (4) : 457-474. doi: 10.3934/cpaa.2002.1.457 |
[20] |
Olivier Goubet, Ezzeddine Zahrouni. Global attractor for damped forced nonlinear logarithmic Schrödinger equations. Discrete and Continuous Dynamical Systems - S, 2021, 14 (8) : 2933-2946. doi: 10.3934/dcdss.2020393 |
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