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Journal of Advances in Applied Mathematics
JAAM > Volume 6, Number 1, January 2021

Weak Nontrivial Solutions to Discrete Nonlinear Two-Point Boundary-Value Problems of Kirchhoff Type

Download PDF  (213.7 KB)PP. 1-14,  Pub. Date:January 12, 2021
DOI: 10.22606/jaam.2021.61001

Author(s)
Rodrigue SANOU, Idrissa IBRANGO, Blaise KONÉ
Affiliation(s)
Laboratoire de Mathématiques et Informatique (LAMI), UFR, Sciences Exactes et Appliquées, Université Joseph-Ki-ZERBO, 03 BP 7021 Ouaga 03, Ouagadougou, Burkina-Faso
Laboratoire de Mathématiques et Informatique (LAMI), UFR, Sciences et Technique, Université Nazi BONI, 01 BP 1091 Bobo 01, Bobo Dioulasso, Burkina-Faso
Laboratoire de Mathématiques et Informatique (LAMI), Institut Burkinabé des Arts et Métiers, Université Joseph-Ki-ZERBO, 03 BP 7021 Ouaga 03, Ouagadougou, Burkina-Faso
Abstract
We prove the existence of at least one weak nontrivial solutions for a discrete nonlinear two-point boundary-value problems of Kirchhoff type. The main existence results are obtained by using the technique of geometric mountain pass and the Ekelands variational principle.
Keywords
discrete boundary value problem, critical point, weak solution, mountain pass geometry lemma, Palais-Smale condition
References
  • [1]  1. S.N. Elaydi, An Introduction to Difference Equations, Undergraduate Texts in Mathematics, Springer- Verlag,New York, 1999.
  • [2]  2. V. Lakshmikantham and D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications, Academic Press, New York, 1988.
  • [3]  3. D.W. Oplinger; Frequency response of a nonlinear stretched string, J. Acoustic Soc. Amer 32(1960), 1529- 1538.
  • [4]  4. Blaise Koné and Stanislas Ouaro; On the Solvability of Discrete Nonlinear Two-Point Boundary Value Problems International Journal of Mathematics and Mathematical Sciences; Vol. 2012.
  • [5]  5. Blaise Koné, Ismael Nyanquini and Stanislas Ouaro; Weak Solutions to Discrete Nonlinear Two-Point Boundary-Value Problems of Kirchhoff Type, Electronic Journal of Differential Equations, Vol. 2015(2015), No. 105, pp. 1-10.
  • [6]  6. X. Cai and J. Yu; Existence theorems for second-order discrete boundary value problems, J. Math. Anal. Appl. 320 (2006), 649-661.
  • [7]  7. M. Mihailescu, V. Radulescu and S. Tersian; Eigenvalue problems for anisotropic discrete boundary value problems, J. Differ. Equ. Appl. 15 (2009), 557-567.
  • [8]  8. Marek Galewski and Renata Wieteska.Multiple periodic solutions to a discrete p(k)- Laplacian problem.
  • [9]  9. J. Mawhin, Problèmes de Dirichlet variationnels non linéaires, Les Presses de l’Université de Montréal, 1987.
  • [10]  10. De Figueiredo DG. Lectures on the Ekeland Variational Principe with Applications and Detours. Bombay: Tata Institute of Fundamental Research, 1989.
  • [11]  11. Dajun G. Nonlinear Functional Analysis. Shandong Science and Technology Press, 1985.
  • [12]  12. Borwein JM, Lewis As. Convex analysis and nonlinear optimization. Theory and examples. 2nd ed., CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC 3. New York, NY: Springer. Xii, 2006.
  • [13]  13. Rodrigue Sanou, Idrissa Ibrango,Blaise Koné and Aboudramane Guiro; Weak Solutions to Neumann discrete nonlinear System of Kirchhoff type, Cubo A Mathematical Journal, Vol.21, num 03, (75-91). December 2019.
  • [14]  14. Idrissa Ibrango, Rodrigue Sanou, Blaise Koné and Aboudramane Guiro; Weak Homoclinic Solutions of Anisotropic Discrete nonlinear System with Variable Exponent, Nonauton.Dyn.Syst.2020.
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