Multiplicity and concentration of positive solutions for fractional nonlinear Schrödinger equation

Xudong Shang;  ; Jihui Zhang;

doi:10.3934/cpaa.2018107

Multiplicity and concentration of positive solutions for fractional nonlinear Schrödinger equation

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2018107 ◽

2018 ◽

Vol 17 (6) ◽

pp. 2239-2259

Author(s):

Xudong Shang ◽

◽

Jihui Zhang ◽

Keyword(s):

Schrödinger Equation ◽

Positive Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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Multi-bump positive solutions of a fractional nonlinear Schrödinger equation in $\mathbb{R}^N$

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2016.15.413 ◽

2016 ◽

Vol 15 (2) ◽

pp. 413-428

Author(s):

Weiming Liu ◽

Lu Gan

Keyword(s):

Schrödinger Equation ◽

Positive Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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Existence and concentration of positive solutions for fractional nonlinear Schrödinger equation with critical growth

Journal of Mathematical Physics ◽

10.1063/1.4996578 ◽

2017 ◽

Vol 58 (8) ◽

pp. 081502

Author(s):

Xudong Shang ◽

Jihui Zhang

Keyword(s):

Schrödinger Equation ◽

Positive Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Critical Growth ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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Existence of positive solutions with peaks on a Clifford torus for a fractional nonlinear Schrödinger equation

Science China Mathematics ◽

10.1007/s11425-017-9195-4 ◽

2018 ◽

Vol 62 (9) ◽

pp. 1731-1748

Author(s):

Weiming Liu ◽

Lu Gan

Keyword(s):

Schrödinger Equation ◽

Positive Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Clifford Torus ◽

Nonlinear Schrödinger ◽

Existence Of Positive Solutions ◽

Fractional Nonlinear Schrödinger Equation

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Multi-peak solutions to fractional nonlinear Schrödinger equation with general nonlinearity

Complex Variables and Elliptic Equations ◽

10.1080/17476933.2021.1900138 ◽

2021 ◽

pp. 1-26

Author(s):

Xudong Shang ◽

Pei Ma ◽

Jihui Zhang

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

General Nonlinearity ◽

Fractional Nonlinear Schrödinger Equation

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A Fast Conservative Scheme for the Space Fractional Nonlinear Schrödinger Equation with Wave Operator

Journal of Mathematical Study ◽

10.4208/jms.v54n4.21.06 ◽

2021 ◽

Vol 54 (4) ◽

pp. 407-426

Author(s):

MustafaAlmushaira & FeiLiu

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Wave Operator ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Conservative Scheme ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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Global existence and blowup on the energy space for the inhomogeneous fractional nonlinear Schrödinger equation

Discrete & Continuous Dynamical Systems - B ◽

10.3934/dcdsb.2018323 ◽

2019 ◽

Vol 24 (7) ◽

pp. 3335-3356 ◽

Cited By ~ 1

Author(s):

Congming Peng ◽

◽

Dun Zhao ◽

Keyword(s):

Global Existence ◽

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Energy Space ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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Dynamical behavior and exact solutions for time-fractional nonlinear Schrödinger equation with parabolic law nonlinearity

Optik ◽

10.1016/j.ijleo.2020.165331 ◽

2020 ◽

Vol 222 ◽

pp. 165331

Author(s):

Cheng Chen ◽

Yaolin Jiang ◽

Zuolei Wang ◽

Juanjuan Wu

Keyword(s):

Schrödinger Equation ◽

Exact Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Dynamical Behavior ◽

Nonlinear Schrodinger Equation ◽

Nonlinear Schrödinger ◽

Parabolic Law ◽

Fractional Nonlinear Schrödinger Equation ◽

Parabolic Law Nonlinearity

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Positive solutions of nonlinear Schrödinger equation with peaks on a Clifford torus

Mathematische Nachrichten ◽

10.1002/mana.201400321 ◽

2016 ◽

Vol 289 (8-9) ◽

pp. 1131-1147 ◽

Cited By ~ 1

Author(s):

Sanjiban Santra ◽

Juncheng Wei

Keyword(s):

Schrödinger Equation ◽

Positive Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Clifford Torus ◽

Nonlinear Schrödinger

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Multiple positive solutions for a nonlinear Schrödinger equation

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/pl00001511 ◽

2000 ◽

Vol 51 (3) ◽

pp. 366-384 ◽

Cited By ~ 65

Author(s):

Th. BartschRID="*" ◽

Z.-Q. WangRID="*"ID="*"Research supported

Keyword(s):

Schrödinger Equation ◽

Positive Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Multiple Positive Solutions ◽

Nonlinear Schrödinger

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Vector optical soliton and periodic solutions of a coupled fractional nonlinear Schrödinger equation

Results in Physics ◽

10.1016/j.rinp.2020.103036 ◽

2020 ◽

Vol 17 ◽

pp. 103036 ◽

Cited By ~ 18

Author(s):

Ben-Hai Wang ◽

Peng-Hong Lu ◽

Chao-Qing Dai ◽

Yi-Xiang Chen

Keyword(s):

Schrödinger Equation ◽

Periodic Solutions ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Nonlinear Schrodinger Equation ◽

Optical Soliton ◽

Nonlinear Schrödinger ◽

Fractional Nonlinear Schrödinger Equation

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