Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 15
228
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Multiple positive solutions for a class of Kirchhoff equation on bounded domain

&

References

  • Li F, Zhang Y, Zhu X, et al. Ground-state solutions to Kirchhoff-type transmission problems with critical perturbation. J Math Anal Appl. Feb 2020;482(2):123568.
  • Xu H. Existence of positive solutions for the nonlinear Kirchhoff type equations in Rn. J Math Anal Appl. Feb 2020;482(2):123593.
  • Chen S, Zhang B, Tang X. Existence and non-existence results for Kirchhoff-type problems with convolution nonlinearity. Adv Nonlinear Anal. Sep 2018;9(1):148–167.
  • Tang XH, Chen S. Ground state solutions of Nehari–Pohozaev type for Kirchhoff-type problems with general potentials. Calc Var Partial Differ Equ. Jul 2017;56(4):1–25.
  • Tang XH, Cheng B. Ground state sign-changing solutions for Kirchhoff type problems in bounded domains. J Differ Equ. Aug 2016;261(4):2384–2402.
  • Zhang H, Zhang F. Ground states for the nonlinear Kirchhoff type problems. J Math Anal Appl. Mar 2015;423(2):1671–1692.
  • Junior JRS. The effect of the domain topology on the number of positive solutions of an elliptic Kirchhoff problem. Nonlinear Anal Real World Appl. Apr 2016;28:269–283.
  • Zhang J, Sun J, Wu TF. The number of positive solutions affected by the weight function to Kirchhoff type equations in high dimensions. Nonlinear Anal. Jul 2020;196:111780.
  • Xie W, Chen H. Multiple positive solutions for the critical Kirchhoff type problems involving sign-changing weight functions. J Math Anal Appl. Nov 2019;479(1):135–161.
  • Li Q, Teng K, Wang W, et al. Concentration phenomenon of solutions for a class of Kirchhoff-type equations with critical growth. J Math Anal Appl. Nov 2020;491(2):124355.
  • Lin X, Wei J. Existence and concentration of ground state solutions for a class of Kirchhoff-type problems. Nonlinear Anal. Jun 2020;195:111715.
  • Gu G, Tang X. The concentration behavior of ground states for a class of Kirchhoff-type problems with hartree-type nonlinearity. Adv Nonlinear Stud. Nov 2019;19(4):779–795.
  • Shang X, Zhang J. Existence and concentration of bound states for a Kirchhoff type problem with potentials vanishing or unbounded at infinity. Math Methods Appl Sci. Feb 2018;41(8):3018–3043.
  • Alimohammady M, Alves CO, Amiri HK. Existence and multiplicity of positive solutions for a class of Kirchhoff Laplacian type problems. J Math Phys. Oct 2019;60(10):101503.
  • Li F, Gao C, Liang Z, et al. Existence and concentration of nontrivial nonnegative ground state solutions to Kirchhoff-type system with Hartree-type nonlinearity. Zeitschrift Für Angewandte Mathematik Und Physik. Nov 2018;69(6):1–20.
  • Siciliano G. Multiple positive solutions for a Schrödinger–Poisson–Slater system. J Math Anal Appl. May 2010;365(1):288–299.
  • Ghimenti M, Pagliardini D. Multiple positive solutions for a slightly subcritical Choquard problem on bounded domains. Calc Var Partial Differ Equ. Sep 2019;58(5):3943.
  • Willem M. Minimax theorems. Boston: Birkhäuser; 1997.
  • Xie Q, Ma S, Zhang X. Bound state solutions of Kirchhoff type problems with critical exponent. J Differ Equ. Jul 2016;261(2):890–924.
  • James IM. On category. in the sense of Lusternik–Schnirelmann. Topology. 1978;17(4):331–348.
  • Benci V, Cerami G, Passaseo D. On the number of the positive solutions of some nonlinear elliptic problems. Nonlinear Anal. 1991;26:93–107.
  • Struwe M. Variational methods. Berlin: Springer; 2008.
  • Naimen D. The critical problem of Kirchhoff type elliptic equations in dimension four. J Differ Equ. Aug 2014;257(4):1168–1193.
  • Benci V, Bonanno C, Micheletti AM. On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds. J Funct Anal. Nov 2007;252(2):464–489.

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:

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:

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.