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Three solutions for discrete anisotropic Kirchhoff-type problems

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Języki publikacji
EN
Abstrakty
EN
In this article, using critical point theory and variational methods, we investigate the existence of at least three solutions for a class of double eigenvalue discrete anisotropic Kirchhoff-type problems. An example is presented to demonstrate the applicability of our main theoretical findings.
Wydawca
Rocznik
Strony
art. no. 20220209
Opis fizyczny
Bibliogr. 29 poz.
Twórcy
  • Department of Mathematics and Statistics, Missouri S&T, Rolla, MO 65409, USA
  • Department of Economics, University of Messina, Messina, Italy
  • Department of Mathematics, Razi University, Faculty of Sciences, 67149 Kermanshah, Iran
  • Department of Mathematics, Razi University, Faculty of Sciences, 67149 Kermanshah, Iran
Bibliografia
  • [1] G. R. Kirchhoff, Vorlesungen über Mechanik, Teubner, Leipzig, 1883.
  • [2] J.-L. Lions, On some questions in boundary value problems of mathematical physics, In: Contemporary Developments in Continuum Mechanics and Partial Differential Equations (Proc. Internat. Sympos., Inst. Mat., Univ. Fed. Rio de Janeiro, Rio de Janeiro, 1977), volume 30 of North-Holland Math. Stud., Amsterdam-New York, North-Holland, 1978, pp. 284–346.
  • [3] A. Arosio and S. Panizzi, On the well-posedness of the Kirchhoff string, Trans. Amer. Math. Soc. 348 (1996), no. 1, 305–330.
  • [4] S. Heidarkhani and A. Salari, Existence of three solutions for Kirchhoff-type three-point boundary value problems, Hacet. J. Math. Stat. 50 (2021), no. 2, 304–317.
  • [5] G. A. Afrouzi, S. Heidarkhani, and S. Moradi, Multiple solutions for a Kirchhoff-type second-order impulsive differential equation on the half-line, Quaest. Math. 45 (2022), no. 1, 109–141.
  • [6] S. Heidarkhani, A. L. A. De Araujo, G. A. Afrouzi, and S. Moradi, Existence of three weak solutions for Kirchhoff-type problems with variable exponent and nonhomogeneous Neumann conditions, Fixed Point Theory 21 (2020), no. 2, 525–547.
  • [7] P. D’Ancona and S. Spagnolo, Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math. 108 (1992), no. 2, 247–262.
  • [8] M. Galewski, G. M. Bisci, and R. Wieteska, Existence and multiplicity of solutions to discrete inclusions with the p(k)-Laplacian problem, J. Difference Equ. Appl. 21 (2015), no. 10, 887–903.
  • [9] L.-H. Bian, H.-R. Sun, and Q.-G. Zhang, Solutions for discrete p-Laplacian periodic boundary value problems via critical point theory, J. Difference Equ. Appl. 18 (2012), no. 3, 345–355.
  • [10] X. Cai and J. Yu, Existence theorems for second-order discrete boundary value problems, J. Math. Anal. Appl. 320 (2006), no. 2, 649–661.
  • [11] Y. Tian, Z. Du, and W. Ge, Existence results for discrete Sturm-Liouville problem via variational methods, J. Difference Equ. Appl. 13 (2007), no. 6, 467–478.
  • [12] J. Yu and Z. Guo, On boundary value problems for a discrete generalized Emden-Fowler equation, J. Differential Equations 231 (2006), no. 1, 18–31.
  • [13] O. Chakrone, E. M. Hssini, M. Rahmani, and O. Darhouche, Multiplicity results for a p-Laplacian discrete problems of Kirchhoff type, Appl. Math. Comput. 276 (2016), 310–315.
  • [14] S. Heidarkhani, G. Caristi, and A. Salari, Perturbed Kirchhoff-type p-Laplacian discrete problems, Collect. Math. 68 (2017), no. 3, 401–418.
  • [15] S. Heidarkhani, G. A. Afrouzi, J. Henderson, S. Moradi, and G. Caristi, Variational approaches to p-Laplacian discrete problems of Kirchhoff-type, J. Difference Equ. Appl. 23 (2017), no. 5, 917–938.
  • [16] S. Heidarkhani, G. A. Afrouzi, S. Moradi, and G. Caristi, Critical point approaches to difference equations of Kirchhoff-type, In: Differential and Difference Equations with Applications, volume 230 of Springer Proc. Math. Stat., Springer, Cham, 2018, pp. 39–51.
  • [17] Z. Yücedağ, Existence of solutions for anisotropic discrete boundary value problems of Kirchhoff type, Int. J. Differ. Equ. Appl. 13 (2014), no. 1, 1–15.
  • [18] J. R. Graef, S. Heidarkhani, L. Kong, and S. Moradi, On an anisotropic discrete boundary value problem of Kirchhoff type, J. Difference Equ. Appl. 27 (2021), no. 8, 1103–1119.
  • [19] J. R. Graef, L. Kong, S. Heidarkhani, and S. Moradi, Infinitely many solutions for anisotropic discrete boundary value problems of Kirchhoff type, Int. J. Difference Equ. 15 (2020), no. 2, 389–401.
  • [20] M. Avci, Solutions to a system of p k( )-Kirchhoff discrete boundary value problems, Nonlinear Stud. 23 (2016), no. 4, 665–674.
  • [21] A. Guiro, I. Ibrango, and S. Ouaro, Weak heteroclinic solutions of discrete nonlinear problems of Kirchhoff type with variable exponent, Nonlinear Dyn. Syst. Theory, 18 (2018), no. 1, 67–79.
  • [22] R. Sanou, I. Ibrango, B. Koné, and A. Guiro, Weak solutions to Neumann discrete nonlinear system of Kirchhoff type, Cubo, 21 (2019), no. 3, 75–91.
  • [23] Z. Yücedağ, Solutions for a discrete boundary value problem involving Kirchhoff type equation via variational methods, TWMS J. Appl. Eng. Math. 8 (2018), no. 1, 144–154.
  • [24] G. Bonanno and P. Candito, Non-differentiable functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations, 244 (2008), no. 12, 3031–3059.
  • [25] S. Heidarkhani, G. A. Afrouzi, S. Moradi, and G. Caristi, Existence of three solutions for multi-point boundary value problems, J. Nonlinear Funct. Anal. 2017 (2017), 1–19, Art. ID 47.
  • [26] S. Heidarkhani, A. Cabada, G. A. Afrouzi, S. Moradi, and G. Caristi, A variational approach to perturbed impulsive fractional differential equations, J. Comput. Appl. Math., 341 (2018), 42–60.
  • [27] S. Heidarkhani, G. A. Afrouzi, M. Ferrara, and S. Moradi, Variational approaches to impulsive elastic beam equations of Kirchhoff type, Complex Var. Elliptic Equ. 61 (2016), no. 7, 931–968.
  • [28] S. Heidarkhani, S. Moradi, and S. A. Tersian, Three solutions for second-order boundary-value problems with variable exponents, Electron. J. Qual. Theory Differ. Equ. 2018 (2018), Paper No. 33, 1–19.
  • [29] M. Galewski and R. Wieteska, Existence and multiplicity of positive solutions for discrete anisotropic equations, Turkish J. Math. 38 (2014), no. 2, 297–310.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-4a4d59da-10f7-44b0-8d17-5287df7ebde7
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