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Existence and Multiplicity of Solutions for a Class of Quasilinear Schrödinger Equations ♦

Received: 22 June 2022     Accepted: 8 July 2022     Published: 26 July 2022
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Abstract

Quasilinear Schrödinger equations appear in several differential physical phenomena. We consider the quasilinear Schrödinger equation , where V and f are periodic in x1,...,xN and f is odd in u and subcritical. By employing the genus theory and variational method, we only need f is continuous, which is allowed to have weaker asymptotic growth than usually assumed, and obtain infinitely many geometrically distinct solutions for λ > 0.

Published in American Journal of Applied Mathematics (Volume 10, Issue 4)
DOI 10.11648/j.ajam.20221004.12
Page(s) 125-133
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Quasilinear Schrodinger Equation, Multiplicity of Solutions, Genus Theory

References
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  • APA Style

    Ziqing Yuan, Shen Liu. (2022). Existence and Multiplicity of Solutions for a Class of Quasilinear Schrödinger Equations ♦. American Journal of Applied Mathematics, 10(4), 125-133. https://doi.org/10.11648/j.ajam.20221004.12

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    ACS Style

    Ziqing Yuan; Shen Liu. Existence and Multiplicity of Solutions for a Class of Quasilinear Schrödinger Equations ♦. Am. J. Appl. Math. 2022, 10(4), 125-133. doi: 10.11648/j.ajam.20221004.12

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    AMA Style

    Ziqing Yuan, Shen Liu. Existence and Multiplicity of Solutions for a Class of Quasilinear Schrödinger Equations ♦. Am J Appl Math. 2022;10(4):125-133. doi: 10.11648/j.ajam.20221004.12

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  • @article{10.11648/j.ajam.20221004.12,
      author = {Ziqing Yuan and Shen Liu},
      title = {Existence and Multiplicity of Solutions for a Class of Quasilinear Schrödinger Equations ♦},
      journal = {American Journal of Applied Mathematics},
      volume = {10},
      number = {4},
      pages = {125-133},
      doi = {10.11648/j.ajam.20221004.12},
      url = {https://doi.org/10.11648/j.ajam.20221004.12},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20221004.12},
      abstract = {Quasilinear Schrödinger equations appear in several differential physical phenomena. We consider the quasilinear Schrödinger equation , where V and f are periodic in x1,...,xN and f is odd in u and subcritical. By employing the genus theory and variational method, we only need f is continuous, which is allowed to have weaker asymptotic growth than usually assumed, and obtain infinitely many geometrically distinct solutions for λ > 0.},
     year = {2022}
    }
    

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    T1  - Existence and Multiplicity of Solutions for a Class of Quasilinear Schrödinger Equations ♦
    AU  - Ziqing Yuan
    AU  - Shen Liu
    Y1  - 2022/07/26
    PY  - 2022
    N1  - https://doi.org/10.11648/j.ajam.20221004.12
    DO  - 10.11648/j.ajam.20221004.12
    T2  - American Journal of Applied Mathematics
    JF  - American Journal of Applied Mathematics
    JO  - American Journal of Applied Mathematics
    SP  - 125
    EP  - 133
    PB  - Science Publishing Group
    SN  - 2330-006X
    UR  - https://doi.org/10.11648/j.ajam.20221004.12
    AB  - Quasilinear Schrödinger equations appear in several differential physical phenomena. We consider the quasilinear Schrödinger equation , where V and f are periodic in x1,...,xN and f is odd in u and subcritical. By employing the genus theory and variational method, we only need f is continuous, which is allowed to have weaker asymptotic growth than usually assumed, and obtain infinitely many geometrically distinct solutions for λ > 0.
    VL  - 10
    IS  - 4
    ER  - 

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Author Information
  • Department of Mathematics, Shaoyang University, Shaoyang, Hunan, P. R. China

  • Big Data College Tongren University, Tongren, Guizhou, P. R. China

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