Weak solutions to Neumann discrete nonlinear system of Kirchhoff type
- Rodrigue Sanou drigoaime@gmail.com
- Idrissa Ibrango ibrango2006@yahoo.fr
- Blaise Koné leizon71@yahoo.fr
- Aboudramane Guiro abouguiro@yahoo.fr
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DOI:
https://doi.org/10.4067/S0719-06462019000300075Abstract
We prove the existence of weak solutions for discrete nonlinear system of Kirchhoff type. We build some Hilbert spaces with suitable norms. We define the notion of weak solution corresponding to the problem (1.1). The proof of the main result is based on a minimization method of an energy functional J.
Keywords
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[6] A. Guiro, I. Nyanquini and S. Ouaro; On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian, Adv. Differ. equ. 32 (2011).
[7] B. Koné and S. Ouaro; Weak solutions for anisotropic discrete boundary value problems, J. Differ. Equ. Appl. 16(2) (2010), 1-11.
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[11] Z. Yucedag; Existence of solutions for anisotropic discrete boundary value problems of Kirchhoff type, Int. J. Differ. Equ. Appl, Vol. 13(1) (2014), 1-15.
[12] G. Zhang and S. Liu; On a class of semi-positone discrete boundary value problem, J. Math. Anal. Appl. 325 (2007), 175-182.
[13] J. Zhao; Positive solutions and eigenvalue intervals for a second order p-Laplacian discrete system, Adv. Differ. equ. 2018 2018:281.
[14] V. Zhikov; Averaging of functionals in the calculus of variations and elasticity, Mathematics of the USSR-Izvestiya, vol.29 (1987), pp. 33-66.
[2] X. Cai and J. Yu; Existence theorems for second-order discrete boundary value problems, J. Math. Anal. Appl. 320 (2006), 649-661.
[3] A. Castro and R. Shivaji; Non-negative solutions for a class of radically symmetric non-positone problems, Proceedings of the American Mathematical Society, vol 106, pp. 735-740, 1989.
[4] Y. Chen, S. Levine, and M.Rao; Variable exponent, linear growth functionals in image restoration, SIAM Journal on Applied Mathematics, vol. 66, no. 4, pp. 1383-1406, 2006.
[5] L. Diening; Theoretical and numerical results for electrorheogica fluids, [PhD. thesis], University of Freiburg, 2002.
[6] A. Guiro, I. Nyanquini and S. Ouaro; On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian, Adv. Differ. equ. 32 (2011).
[7] B. Koné and S. Ouaro; Weak solutions for anisotropic discrete boundary value problems, J. Differ. Equ. Appl. 16(2) (2010), 1-11.
[8] M. Mihailescu, V. Radulescu and S. Tersian; Eigenvalue problems for anisotropic discrete boundary value problems, J. Differ. Equ. Appl. 15 (2009), 557-567.
[9] K. R. Rajagopal and M. Ruzicka; Mathematical modeling of electrorheological materials, Continuum Mechanics and Thermodynamics, vol.13, pp.59-78, 2001.
[10] M. Ruzicka, Electrorheological Fluids; Modeling and Mathematical Theory, vol. 1748 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 2000.
[11] Z. Yucedag; Existence of solutions for anisotropic discrete boundary value problems of Kirchhoff type, Int. J. Differ. Equ. Appl, Vol. 13(1) (2014), 1-15.
[12] G. Zhang and S. Liu; On a class of semi-positone discrete boundary value problem, J. Math. Anal. Appl. 325 (2007), 175-182.
[13] J. Zhao; Positive solutions and eigenvalue intervals for a second order p-Laplacian discrete system, Adv. Differ. equ. 2018 2018:281.
[14] V. Zhikov; Averaging of functionals in the calculus of variations and elasticity, Mathematics of the USSR-Izvestiya, vol.29 (1987), pp. 33-66.
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Published
2020-01-20
How to Cite
[1]
R. Sanou, I. Ibrango, B. Koné, and A. Guiro, “Weak solutions to Neumann discrete nonlinear system of Kirchhoff type”, CUBO, vol. 21, no. 3, pp. 75–91, Jan. 2020.
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