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

Ziqing Yuan; Shen Liu

doi:doi:10.11648/j.ajam.20221004.12

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

Ziqing Yuan, Shen Liu

Published in American Journal of Applied Mathematics (Volume 10, Issue 4)

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,...,x^N 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
Creative Commons	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), 2024. Published by Science Publishing Group

Keywords

Quasilinear Schrodinger Equation, Multiplicity of Solutions, Genus Theory

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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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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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TY  - JOUR
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

Ziqing Yuan

Department of Mathematics, Shaoyang University, Shaoyang, Hunan, P. R. China
Shen Liu

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

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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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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  -

Copy | Download