On a class of nonlinear discrete problems of Kirchhoff type

Authors

DOI:

https://doi.org/10.24193/subbmath.2025.4.10

Keywords:

Anisotropic problem, discrete boundary value problem, variational methods, Kirchhoff-type problem

Abstract

In view of variational methods and critical points theory, we study the existence of solutions for a discrete boundary value problem, which is a discrete variant of a continuous (p1(x), p2(x))-Kirchhoff-type problem, with a real parameter λ > 0.

Mathematics Subject Classification (2010): 39A27, 35J25, 39A14, 35J58.

Received 17 March 2025; Accepted 10 June 2025.

References

[1] Agarwal, R.P., Perera K., D. O'Regan D., Multiple positive solutions of singular and nonsingular discrete problems via variational methods. Nonlinear Anal. 58 (2004), no 1-2, 69-73.

[2] Arosio, A., Panizzi, S., On the well-posedness of the Kirchhoff string, Trans. Amer. Math. Soc. 348 (1996), no. 1, 305-330.

[3] Avci, M., Existence and multiplicity of solutions for Dirichlet problems involving the p(x)-Laplace operator, Electron. J. Differential Equations, 2013 (2013), no. 14 1-9.

[4] Avci, M., Ayazoglu, R., Solutions of Nonlocal (p₁(x), p₂(x))-Laplacian Equations, J. Partial Differ. Equ. 14 (2013), Article ID 364251.

[5] Avci, M., On a nonlocal Neumann problem in Orlicz-Sobolev spaces, J. Nonlinear Funct. Anal. 2017 (2017), no. 42, 1-11.

[6] Cai, X., Yu, J., Existence theorems for second-order discrete boundary value problems, J. Math. Anal. Appl. 320 (2006), no. 2 649-661.

[7] Cavalcanti, M.M., Domingos Cavalcanti, V.N., Soriano, J.A., Global existence and uniform decay rates for the Kirchhoff-Carrier equation with nonlinear dissipation, Adv. Differential Equations, 6 (2001), no. 6, 701-730.

[8] Chen, Y., Levine, S., Rao, M., Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006), no. 4, 1383-1406.

[9] Chung, N., Multiplicity results for a class of p(x)-Kirchhoff type equations with combined nonlinearities, Electron. J. Qual. Theory Differ. Equ. 2012 (2012), no. 42, 1-13.

[10] D'Ancona, P., Spagnolo, S., Global solvability for the degenerate Kirchhoff equation with real analytic data, Invent. Math. 108 (1992), no. 1, 247-262.

[11] Dreher, M., The Kirchhoff equation for the p-Laplacian, Rend. Semin. Mat. Univ. Politec. Torino. 64 (2006), no. 2, 217-238.

[12] Ekeland, I., On the variational principle, J. Math. Anal. Appl. 47 (1974), no. 2, 324-353.

[13] Galewski, M., Wieteska, R., On the system of anisotropic discrete BVPs, J. Difference Equ. Appl. 19 (2013), no. 7, 1065-1081.

[14] Kirchhoff, G., Vorlesungen über mathematische Physik, BG Teubner, 1891.

[15] Mihăilescu, M., Rădulescu, V., Tersian, S., Eigenvalue problems for anisotropic discrete boundary value problems, J. Difference Equ. Appl. 15 (2009), no. 6, 557-56.

[16] Ruzicka, M., Flow of shear dependent electrorheological fluids, Comptes Rendus de l'Académie des Sciences-Series I-Mathematics. 329 (1999), no. 5, 393-398.

[17] Ruzicka, M., Electrorheological fluids: modeling and mathematical theory, Springer, 2007.

[18] Willem, M., Linking theorem, Minimax Theorems, Birkhäuser, Boston, 1996.

[19] Yücedağ, Z., Existence of solutions for anisotropic discrete boundary value problems of Kirchhoff type, J. Difference Equ. Appl. 13 (2014), no. 1, 1-15.

[20] Yücedağ, Z., 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.

[21] Zhikov, V.V.E., Averaging of functionals of the calculus of variations and elasticity theory, Izv. Math. 29 (1987), no. 1, 33-66.

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Published

2025-12-09

How to Cite

BARGHOUTHE, M., AYOUJIL, A., & BERRAJAA, M. (2025). On a class of nonlinear discrete problems of Kirchhoff type. Studia Universitatis Babeș-Bolyai Mathematica, 70(4), 671–683. https://doi.org/10.24193/subbmath.2025.4.10

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