Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 10
Submit an article Journal homepage
104
Views
2
CrossRef citations to date
0
Altmetric
Research Article

Existence of positive ground state solutions for quasilinear Schrödinger system with positive parameter

Jianqing Chena School of Mathematics and Statistics, Fujian Normal University, Fuzhou, People's Republic of China;b FJKLMAA and Center for Applied Mathematics of Fujian Province (FJNU), Fuzhou, People's Republic of ChinaView further author information
&
Qian Zhanga School of Mathematics and Statistics, Fujian Normal University, Fuzhou, People's Republic of ChinaCorrespondence[email protected]
View further author information
Pages 2676-2691 | Received 13 Oct 2021, Accepted 17 Jan 2022, Published online: 01 Feb 2022

References

  • Borovskii A, Galkin A. Dynamical modulation of an ultrashort high-intensity laser pulse in matter. J Exp Theor Phys. 1993;77:562–573.
  • Bouard A, Hayashi N, Saut J. Global existence of small solutions to a relativistic nonlinear Schrödinger equation. Commun Math Phys. 1997;189(1):73–105.
  • Brandi H, Manus C, Mainfray G, et al. Relativistic and ponderomotive self-focusing of a laser beam in a radially inhomogeneous plasma. I: paraxial approximation. Phys Fluids B. 1993;5(10):3539–3550.
  • Brézis H, Lieb E. A relation between pointwise convergence of function and convergence of functional. Proc Amer Math Soc. 1983;88(3):486–490.
  • Brüll L, Lange H. Solitary waves for quasilinear Schrödinger equations. Expos Math. 1986;4:278–288.
  • Kurihura S. Large-amplitude quasi-solitons in superfluids films. J Phys Soc Jpn. 1981;50(10):3262–3267.
  • Schott M. Stationäre Lösungen quasilinearer Schrödinger-Gleichungen [Diploma Thesis]. Universitèt Köln; 2002.
  • Berestycki H, Lions P. Nonlinear scalar field equations, I. Arch Ration Mech Anal. 1983;82(4):313–346.
  • Lions P. The concentration-compactness principle in the calculus of variations. The locally compact case. Part 1-2. Ann Inst H Poincaré. 1984;1(2):109–145 and 223–283.
  • Rabinowitz P. On a class of nonlinear Schrödinger equations. Z Angew Math Phys. 1992;43(2):270–291.
  • Poppenberg M, Schmitt K, Wang Z. On the existence of soliton solutions to quasilinear Schrödinger equations. Calc Var PDE. 2002;14(3):329–344.
  • Liu J, Wang Z. Soliton solutions for quasilinear Schrödinger equations, II. J Differ Equ. 2003;187(2):473–493.
  • Colin M, Jeanjean L. Solutions for a quasilinear Schrödinger equations: a dual approach. Nonlinear Anal. 2004;56(2):213–226.
  • Liu J, Wang Y, Wang Z. Solutions for quasilinear Schrödinger equations via the Nehari method. Commun Partial Diff Equ. 2004;29(5–6):879–901.
  • Silva E, Vieira G. Quasilinear asymptotically periodic Schrödinger equations with critical growth. Calc Var PDE. 2010;39(1–2):1–33.
  • Wang Y. Multiplicity of solutions for singular quasilinear Schrödinger equations with critical exponents. J Math Anal Appl. 2018;458(2):1027–1043.
  • Wang Y, Zhang Y, Shen Y. Multiple solutions for quasilinear Schrödinger equations involving critical exponent. Appl Math Comput. 2010;216:849–856.
  • Wang Y, Zou W. Bound states to critical quasilinear Schrödinger equations. Nonlinear Differ Equ Appl. 2012;19(1):19–47.
  • Alves C, Wang Y, Shen Y. Soliton solutions for a class of quasilinear Schrödinger equations with a parameter.J Differ Equ. 2015;259(1):318–343.
  • Huang C, Jia G. Existence of positive solutions for supercritical quasilinear Schrödinger elliptic equations. J Math Anal Appl. 2019;472(1):705–727.
  • Costa D, Wang Z. Multiplicity results for a class of superlinear elliptic problems. Proc Amer Math Soc. 2005;133(3):787–794.
  • Liu H. Positive solution for a quasilinear elliptic equation involving critical or supercritical exponent. J Math Phys. 2016;57:159–180.
  • Willem M. Minimax theorems. Birkhäuser; 1996.
  • Moroz V, Schaftingen J. Ground states of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics. J Funct Anal. 2013;265(2):153–184.
  • Gilbarg D, Trudinger N. Elliptic partial differential equations of second order. Springer; 2001.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.