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Year 2015, Volume: 28 Issue: 3, 473 - 482, 05.10.2015

Mustafa Aktaş Devrim Çakmak Merve Arıtürk

Abstract

References

  • Aktaş, M. F., Çakmak, D., Tiryaki, A., “A note on Tang and He's paper”, Appl. Math. Comput. 218 (2012), 4867- 4871.
  • Aktaş, M. F., “Lyapunov-type inequalities for a certain class of n-dimensional quasilinear systems”, Electron. J. Differential Equations 67 (2013), 1-8.
  • Atkinson, F. V., “Discrete and Continuous Boundary Problems”, Academic Press, New York, NY, USA, 1964.
  • Cheng, S. S., “A discrete analogue of the inequality of Lyapunov”, Hokkaido Math. J. 12 (1983), 105-112.
  • Çakmak, D., Tiryaki, A., “On Lyapunov-type inequality for quasilinear systems”, Appl. Math. Comput. 216 (2010), 3584-3591.
  • 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.
  • Liapunov, A. M., “Probleme general de la stabilite du mouvement”, Ann. Fac. Sci. Univ. Toulouse 2 (1907), 203- 407.
  • Lin, S. H., Yang, G. S., “On discrete analogue of Lyapunov inequality”, Tamkang J. Math. 20 (1989), 169-186.
  • Tang, X. H., He, X., “Lower bounds for generalized eigenvalues of the quasilinear systems”, J. Math. Anal. Appl. 385 (2012), 72-85.
  • Tiryaki, A., Çakmak, D., Aktaş, M. F., “Lyapunov-type inequalities for a certain class of nonlinear systems”, Comput. Math. Appl. 64 (2012), 1804-1811.
  • Tiryaki, A., Çakmak, D., Aktaş, M. F., “Lyapunov-type inequalities for two classes of Dirichlet quasilinear systems”, Math. Inequal. Appl. 17 (2014), 843-863.
  • Ünal, M., Çakmak, D., Tiryaki, A., “A discrete analogue of Lyapunov-type inequalities for nonlinear systems”, Comput. Math. Appl. 55 (2008), 2631-2642.
  • Wang, Y., Shi, Y., “Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions”, J. Math. Anal. Appl. 309 (2005), 56-69. 482
  • GU J Sci, 28(3):473-482 (2015)/ Mustafa Fahri AKTAŞ, Devrim ÇAKMAK, Merve ARITÜRK
  • Zhang, Q., Tang, X. H., “Lyapunov-type inequalities for quasilinear difference systems”, Discrete Dyn. Nat. Soc. 2012 (2012) Article ID 860598, 16 pages. [15] 25 (2012), 1830-1834.

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

Year 2015, Volume: 28 Issue: 3, 473 - 482, 05.10.2015

Mustafa Aktaş Devrim Çakmak Merve Arıtürk

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

Difference systems Lyapunov-type inequalities Dirichlet boundary conditions

References

  • Aktaş, M. F., Çakmak, D., Tiryaki, A., “A note on Tang and He's paper”, Appl. Math. Comput. 218 (2012), 4867- 4871.
  • Aktaş, M. F., “Lyapunov-type inequalities for a certain class of n-dimensional quasilinear systems”, Electron. J. Differential Equations 67 (2013), 1-8.
  • Atkinson, F. V., “Discrete and Continuous Boundary Problems”, Academic Press, New York, NY, USA, 1964.
  • Cheng, S. S., “A discrete analogue of the inequality of Lyapunov”, Hokkaido Math. J. 12 (1983), 105-112.
  • Çakmak, D., Tiryaki, A., “On Lyapunov-type inequality for quasilinear systems”, Appl. Math. Comput. 216 (2010), 3584-3591.
  • 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.
  • Liapunov, A. M., “Probleme general de la stabilite du mouvement”, Ann. Fac. Sci. Univ. Toulouse 2 (1907), 203- 407.
  • Lin, S. H., Yang, G. S., “On discrete analogue of Lyapunov inequality”, Tamkang J. Math. 20 (1989), 169-186.
  • Tang, X. H., He, X., “Lower bounds for generalized eigenvalues of the quasilinear systems”, J. Math. Anal. Appl. 385 (2012), 72-85.
  • Tiryaki, A., Çakmak, D., Aktaş, M. F., “Lyapunov-type inequalities for a certain class of nonlinear systems”, Comput. Math. Appl. 64 (2012), 1804-1811.
  • Tiryaki, A., Çakmak, D., Aktaş, M. F., “Lyapunov-type inequalities for two classes of Dirichlet quasilinear systems”, Math. Inequal. Appl. 17 (2014), 843-863.
  • Ünal, M., Çakmak, D., Tiryaki, A., “A discrete analogue of Lyapunov-type inequalities for nonlinear systems”, Comput. Math. Appl. 55 (2008), 2631-2642.
  • Wang, Y., Shi, Y., “Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions”, J. Math. Anal. Appl. 309 (2005), 56-69. 482
  • GU J Sci, 28(3):473-482 (2015)/ Mustafa Fahri AKTAŞ, Devrim ÇAKMAK, Merve ARITÜRK
  • Zhang, Q., Tang, X. H., “Lyapunov-type inequalities for quasilinear difference systems”, Discrete Dyn. Nat. Soc. 2012 (2012) Article ID 860598, 16 pages. [15] 25 (2012), 1830-1834.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Mustafa Aktaş

Devrim Çakmak

Merve Arıtürk This is me

Publication Date October 5, 2015
Published in Issue Year 2015 Volume: 28 Issue: 3

Cite

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.
AMA Aktaş M, Çakmak D, Arıtürk M. Lyapunov-Type Inequalities for Two Classes of Difference Systems with Dirichlet Boundary Conditions. Gazi University Journal of Science. October 2015;28(3):473-482.
Chicago Aktaş, Mustafa, Devrim Çakmak, and Merve Arıtürk. “Lyapunov-Type Inequalities for Two Classes of Difference Systems With Dirichlet Boundary Conditions”. Gazi University Journal of Science 28, no. 3 (October 2015): 473-82.
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 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, 2015.
ISNAD Aktaş, Mustafa et al. “Lyapunov-Type Inequalities for Two Classes of Difference Systems With Dirichlet Boundary Conditions”. Gazi University Journal of Science 28/3 (October 2015), 473-482.
JAMA 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, 2015, pp. 473-82.
Vancouver 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):473-82.