Existence and concentration result for a quasilinear Schrödinger equation with critical growth

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-017-0869-6 ◽

2017 ◽

Vol 68 (6) ◽

Author(s):

Liuyang Shao ◽

Haibo Chen

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Critical Growth ◽

Quasilinear Schrödinger Equation ◽

Concentration Result

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Asymptotic property of ground states for a class of quasilinear Schrödinger equation with $$H^1$$-critical growth

Calculus of Variations and Partial Differential Equations ◽

10.1007/s00526-019-1527-y ◽

2019 ◽

Vol 58 (3) ◽

Author(s):

Shinji Adachi ◽

Masataka Shibata ◽

Tatsuya Watanabe

Keyword(s):

Schrödinger Equation ◽

Asymptotic Property ◽

Schrodinger Equation ◽

Ground States ◽

Critical Growth ◽

Quasilinear Schrödinger Equation

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Existence of ground state solutions for a quasilinear Schrödinger equation with critical growth

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2014.11.011 ◽

2015 ◽

Vol 69 (2) ◽

pp. 81-88 ◽

Author(s):

Ke Wu ◽

Fen Zhou

Keyword(s):

Schrödinger Equation ◽

Ground State ◽

Schrodinger Equation ◽

Critical Growth ◽

Quasilinear Schrödinger Equation ◽

Ground State Solutions

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Positive Solutions for a Quasilinear Schrödinger Equation with Critical Growth

Journal of Dynamics and Differential Equations ◽

10.1007/s10884-011-9231-4 ◽

2011 ◽

Vol 24 (1) ◽

pp. 13-28 ◽

Author(s):

Giovany M. Figueiredo ◽

Marcelo F. Furtado

Keyword(s):

Schrödinger Equation ◽

Positive Solutions ◽

Schrodinger Equation ◽

Critical Growth ◽

Quasilinear Schrödinger Equation

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Existence of semiclassical states for a quasilinear Schrödinger equation on ℝ N with exponential critical growth

Acta Mathematica Sinica English Series ◽

10.1007/s10114-016-5488-1 ◽

2016 ◽

Vol 32 (11) ◽

pp. 1279-1296 ◽

Author(s):

Shao Jun Li ◽

Carlos A. Santos ◽

Min Bo Yang

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Critical Growth ◽

Quasilinear Schrödinger Equation ◽

Exponential Critical Growth ◽

Semiclassical States

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Uniqueness of asymptotic limit of ground states for a class of quasilinear Schrödinger equation with H1-critical growth in ℝ3

Applicable Analysis ◽

10.1080/00036811.2020.1757079 ◽

2020 ◽

pp. 1-21

Author(s):

Shinji Adachi ◽

Masataka Shibata ◽

Tatsuya Watanabe

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Ground States ◽

Critical Growth ◽

Asymptotic Limit ◽

Quasilinear Schrödinger Equation

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Multiple minimal nodal solutions for a quasilinear Schrödinger equation with symmetric potential

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2004.09.012 ◽

2005 ◽

Vol 304 (1) ◽

pp. 170-188 ◽

Author(s):

Marcelo F. Furtado

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Nodal Solutions ◽

Quasilinear Schrödinger Equation ◽

Symmetric Potential

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Multiplicity of solutions of the bi-harmonic Schrödinger equation with critical growth

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-018-0940-y ◽

2018 ◽

Vol 69 (2) ◽

Author(s):

Jian Zhang ◽

Zhenluo Lou ◽

Yanju Ji ◽

Wei Shao

Keyword(s):

Schrödinger Equation ◽

Schrodinger Equation ◽

Critical Growth ◽

Multiplicity Of Solutions

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Existence ground state solutions for a quasilinear Schrödinger equation with Hardy potential and Berestycki–Lions type conditions

Applied Mathematics Letters ◽

10.1016/j.aml.2021.107615 ◽

2022 ◽

Vol 123 ◽

pp. 107615

Author(s):

Die Hu ◽

Qi Zhang

Keyword(s):

Schrödinger Equation ◽

Ground State ◽

Schrodinger Equation ◽

Hardy Potential ◽

Quasilinear Schrödinger Equation ◽

Ground State Solutions

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Sharp conditions of global existence for the quasilinear Schrödinger equation

Functional Analysis and Its Applications ◽

10.1007/s10688-008-0019-1 ◽

2008 ◽

Vol 42 (2) ◽

pp. 135-140

Author(s):

J. Zhang ◽

J. Shu

Keyword(s):

Global Existence ◽

Schrödinger Equation ◽

Schrodinger Equation ◽

Quasilinear Schrödinger Equation

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MORAWETZ AND INTERACTION MORAWETZ ESTIMATES FOR A QUASILINEAR SCHRÖDINGER EQUATION

Journal of Hyperbolic Differential Equations ◽

10.1142/s0219891612500208 ◽

2012 ◽

Vol 09 (04) ◽

pp. 613-639 ◽

Author(s):

ALESSANDRO SELVITELLA ◽

YUN WANG

Keyword(s):

Schrödinger Equation ◽

Plasma Physics ◽

Schrodinger Equation ◽

Energy Space ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Quasilinear Schrödinger Equation

We extend the classical Morawetz and interaction Morawetz machinery to a class of quasilinear Schrödinger equations coming from plasma physics. As an application of our main results we ensure the absence of pseudosolitons in the defocusing case. Our estimates are the first step to a scattering result in the energy space for this equation.

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