Publication Cover
Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 16
118
Views
0
CrossRef citations to date
0
Altmetric
Research Article

Nodal solutions for an asymptotically linear Kirchhoff-type problem in ℝN

Pages 4613-4628 | Received 06 Jul 2020, Accepted 22 Sep 2022, Published online: 01 Oct 2022

References

  • Kirchhoff G. Mechanik. Leipzig: Teubner; 1883.
  • Cheng BT, Tang XH. Ground state sign-changing solutions for asymptotically 3-linear Kirchhoff-type problems. Complex Var Elliptic Equ. 2017;62:1093–1116.
  • Figueiredo GM, Nascimento RG. Existence of a nodal solution with minimal energy for a Kirchhoff equation. Math Nachr. 2015;288:48–60.
  • Lu SS. Signed and sign-changing solutions for a Kirchhoff-type equation in bounded domains. J Math Anal Appl. 2015;432:965–982.
  • Mao AM, Luan SX. Sign-changing solutions of a class of nonlocal quasilinear elliptic boundary value problems. J Math Anal Appl. 2011;383:239–243.
  • Mao AM, Zhang ZT. Sign-changing and multiple solutions of Kirchhoff type problems without the P.S. condition. Nonlinear Anal. 2009;70:1275–1287.
  • Shuai W. Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains. J Differ Equ. 2015;259:1256–1274.
  • Shao MQ, Mao AM. Signed and sign-changing solutions of Kirchhoff type problems. J Fixed Point Theory Appl. 2018;20:1–20.
  • Tang XH, Cheng BT. Ground state sign-changing solutions for Kirchhoff type problems in bounded domains. J Differ Equ. 2016;261:2384–2402.
  • Zhang ZT, Perera K. Sign changing solutions of Kirchhoff type problems via invariant sets of descent flow. J Math Anal Appl. 2006;317:456–463.
  • Zhong XJ, Tang CL. The existence and nonexistence results of ground state nodal solutions for a Kirchhoff type problem. Commun Pure Appl Anal. 2017;16:611–627.
  • Chen B, Ou ZQ. Sign-changing and nontrivial solutions for a class of Kirchhoff-type problems. J Math Anal Appl. 2020;481:123476.
  • Cassani D, Liu ZS, Tarsi C, et al. Multiplicity of sign-changing solutions for Kirchhoff-type equations. Nonlinear Anal. 2019;186:145–161.
  • Deng YB, Peng SJ, Shuai W. Existence and asymptotic behavior of nodal solutions for the Kirchhoff-type problems in R3. J Funct Anal. 2015;269:3500–3527.
  • Figueiredo GM, Santos Junior JR. Existence of a least energy nodal solution for a Schrödinger-Kirchhoff equation with potential vanishing at infinity. J Math Phys. 2015;56(5):051506, 18 pp.
  • Isernia T. Sign-changing solutions for a fractional Kirchhoff equation. Nonlinear Anal. 2020;190:111623, 20 pp.
  • Li Q, Du XS, Zhao ZQ. Existence of sign-changing solutions for nonlocal Kirchhoff–Schrödinger-type equations in R3. J Math Anal Appl. 2019;477:174–186.
  • Qin DD, Liao FF, He YB, et al. Infinitely many sign-changing solutions for Kirchhoff-type equations in R3. Bull Malays Math Sci Soc. 2019;42:1055–1070.
  • Sun JJ, Li L, Cencelj M, et al. Infinitely many sign-changing solutions for Kirchhoff type problems R3. Nonlinear Anal. 2019;186:33–54.
  • Wu K, Zhou F. Nodal solutions for a Kirchhoff type problem in RN. Appl Math Lett. 2019;88:58–63.
  • Wang L, Zhang BL, Cheng K. Ground state sign-changing solutions for the Schrödinger-Kirchhoff equation in R3. J Math Anal Appl. 2018;466:1545–1569.
  • Liu ZS, Lou YJ, Zhang JJ. A perturbation approach to studying sign-changing solutions of Kirchhoff equations with a general nonlinearity. Ann Mat Pur Appl. 2021. doi:10.1007/s10231-021-01155-w
  • Costa DG, Magalhaes CA. Variational elliptic problems which are nonquadratic at infinity. Nonlinear Anal. 1994;23:1401–1412.
  • Costa DG. Variational problems which are nonquadratic at infinity. International Press-AMS; 2003. p. 39–56. Preprint for “Proceedings of the Seminar on Morse Theory, Minimax Theory, and Their Applications to Nonlinear Differential Equations”, New Studies in Advanced Mathematics, Vol 1, Editors Haim Brezis, ShuJie Li, JiaQuan Liu, and Paul H. Rabinowitz.
  • Stuart CA. Guidance properties of nonlinear planar waveguides. Arch Rational Mech Anal. 1993;125:145–200.
  • Zhou HS. An application of a mountain pass theorem. Acta Math Sin. 2002;18:27–36.
  • Mata LA, Miyagaki OH, Soares SHM. A sign-changing solution for an asymptotically linear Schrödinger equation. Proc Edinb Math Soc. 2015;58:697–716.
  • Willem M. Minimax theorem. Boston: Birkhauser; 1996.

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.