Research Article

Lyapunov-Type Inequalities for Two Classes of Difference Systems with Dirichlet Boundary Conditions

Volume: 28 Number: 3 October 5, 2015
EN

Lyapunov-Type Inequalities for Two Classes of Difference Systems with Dirichlet Boundary Conditions

Abstract

In this paper, we establish Lyapunov-type inequalities for two classes of difference systems which improve all existing ones in the literature. Applying our inequalities, we obtain a lower bound for the eigenvalues of corresponding systems.

Keywords

References

  1. Aktaş, M. F., Çakmak, D., Tiryaki, A., “A note on Tang and He's paper”, Appl. Math. Comput. 218 (2012), 4867- 4871.
  2. Aktaş, M. F., “Lyapunov-type inequalities for a certain class of n-dimensional quasilinear systems”, Electron. J. Differential Equations 67 (2013), 1-8.
  3. Atkinson, F. V., “Discrete and Continuous Boundary Problems”, Academic Press, New York, NY, USA, 1964.
  4. Cheng, S. S., “A discrete analogue of the inequality of Lyapunov”, Hokkaido Math. J. 12 (1983), 105-112.
  5. Çakmak, D., Tiryaki, A., “On Lyapunov-type inequality for quasilinear systems”, Appl. Math. Comput. 216 (2010), 3584-3591.
  6. Çakmak, D., Tiryaki, A., “Lyapunov-type inequality for a class of Dirichlet quasilinear systems involving the (p₁,p₂,..., )-Laplacian”, J. Math. Anal. Appl. 369 (2010), 76-81.
  7. Liapunov, A. M., “Probleme general de la stabilite du mouvement”, Ann. Fac. Sci. Univ. Toulouse 2 (1907), 203- 407.
  8. Lin, S. H., Yang, G. S., “On discrete analogue of Lyapunov inequality”, Tamkang J. Math. 20 (1989), 169-186.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Publication Date

October 5, 2015

Submission Date

December 26, 2014

Acceptance Date

-

Published in Issue

Year 2015 Volume: 28 Number: 3

APA
Aktaş, M., Çakmak, D., & Arıtürk, M. (2015). Lyapunov-Type Inequalities for Two Classes of Difference Systems with Dirichlet Boundary Conditions. Gazi University Journal of Science, 28(3), 473-482. https://izlik.org/JA42YN92AB
AMA
1.Aktaş M, Çakmak D, Arıtürk M. Lyapunov-Type Inequalities for Two Classes of Difference Systems with Dirichlet Boundary Conditions. Gazi University Journal of Science. 2015;28(3):473-482. https://izlik.org/JA42YN92AB
Chicago
Aktaş, Mustafa, Devrim Çakmak, and Merve Arıtürk. 2015. “Lyapunov-Type Inequalities for Two Classes of Difference Systems With Dirichlet Boundary Conditions”. Gazi University Journal of Science 28 (3): 473-82. https://izlik.org/JA42YN92AB.
EndNote
Aktaş M, Çakmak D, Arıtürk M (October 1, 2015) Lyapunov-Type Inequalities for Two Classes of Difference Systems with Dirichlet Boundary Conditions. Gazi University Journal of Science 28 3 473–482.
IEEE
[1]M. Aktaş, D. Çakmak, and M. Arıtürk, “Lyapunov-Type Inequalities for Two Classes of Difference Systems with Dirichlet Boundary Conditions”, Gazi University Journal of Science, vol. 28, no. 3, pp. 473–482, Oct. 2015, [Online]. Available: https://izlik.org/JA42YN92AB
ISNAD
Aktaş, Mustafa - Çakmak, Devrim - Arıtürk, Merve. “Lyapunov-Type Inequalities for Two Classes of Difference Systems With Dirichlet Boundary Conditions”. Gazi University Journal of Science 28/3 (October 1, 2015): 473-482. https://izlik.org/JA42YN92AB.
JAMA
1.Aktaş M, Çakmak D, Arıtürk M. Lyapunov-Type Inequalities for Two Classes of Difference Systems with Dirichlet Boundary Conditions. Gazi University Journal of Science. 2015;28:473–482.
MLA
Aktaş, Mustafa, et al. “Lyapunov-Type Inequalities for Two Classes of Difference Systems With Dirichlet Boundary Conditions”. Gazi University Journal of Science, vol. 28, no. 3, Oct. 2015, pp. 473-82, https://izlik.org/JA42YN92AB.
Vancouver
1.Mustafa Aktaş, Devrim Çakmak, Merve Arıtürk. Lyapunov-Type Inequalities for Two Classes of Difference Systems with Dirichlet Boundary Conditions. Gazi University Journal of Science [Internet]. 2015 Oct. 1;28(3):473-82. Available from: https://izlik.org/JA42YN92AB