A Note on Multivariate Lyapunov-type Inequality

Volume: 28 Number: 2 June 22, 2015
EN

A Note on Multivariate Lyapunov-type Inequality

Abstract

We transfer the recent obtained result of univariate Lyapunov-type inequality for third order differential equations to the multivariate setting of a shell via the polar method. Our result is better than the result of Anastassiou [Appl. Math. Letters, 24 (2011), 2167-2171] for third order partial differential equations.

Keywords

References

  1. [1] M. F. Aktaş, D. Çakmak, A. Tiryaki, On the Lyapunov-type inequalities of a three-point boundary value problem for third order linear differential equations, Appl. Math. Letters, 45 (2015), 1-6.
  2. [2] M. F. Aktaş, On the multivariate Lyapunov inequalities, Appl. Math. Comput., 232 (2014), 784- 786.
  3. [3] G. A. Anastassiou, Multivariate Lyapunov inequalities, Appl. Math. Letters, 24 (2011), 2167-2171.
  4. [4] A. Canada, J. A. Montero, S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal., 237 (2006), 176-193.
  5. [5] L. Y. Chen, C. J. Zhao, W. S. Cheung, On Lyapunov-type inequalities for two-dimensional nonlinear partial systems, J. Inequal. Appl., 2010, Art. ID 504982, 12 pp.
  6. [6] D. Çakmak, Lyapunov-type integral inequalities for certain higher order differential equations, Appl. Math. Comput., 216 (2010), 368-373.
  7. [7] A. M. Liapunov, Probléme général de la stabilité du mouvement, Ann. Fac. Sci. Univ. Toulouse, 2 (1907), 203-407.
  8. [8] W. Rudin, Real and Complex Analysis, McGrawHill, New York, 1970.

Details

Primary Language

English

Subjects

-

Journal Section

-

Publication Date

June 22, 2015

Submission Date

December 9, 2014

Acceptance Date

-

Published in Issue

Year 2015 Volume: 28 Number: 2

APA
Aktaş, M., & Çakmak, D. (2015). A Note on Multivariate Lyapunov-type Inequality. Gazi University Journal of Science, 28(2), 265-267. https://izlik.org/JA85EA56BJ
AMA
1.Aktaş M, Çakmak D. A Note on Multivariate Lyapunov-type Inequality. Gazi University Journal of Science. 2015;28(2):265-267. https://izlik.org/JA85EA56BJ
Chicago
Aktaş, Mustafa, and Devrim Çakmak. 2015. “A Note on Multivariate Lyapunov-Type Inequality”. Gazi University Journal of Science 28 (2): 265-67. https://izlik.org/JA85EA56BJ.
EndNote
Aktaş M, Çakmak D (June 1, 2015) A Note on Multivariate Lyapunov-type Inequality. Gazi University Journal of Science 28 2 265–267.
IEEE
[1]M. Aktaş and D. Çakmak, “A Note on Multivariate Lyapunov-type Inequality”, Gazi University Journal of Science, vol. 28, no. 2, pp. 265–267, June 2015, [Online]. Available: https://izlik.org/JA85EA56BJ
ISNAD
Aktaş, Mustafa - Çakmak, Devrim. “A Note on Multivariate Lyapunov-Type Inequality”. Gazi University Journal of Science 28/2 (June 1, 2015): 265-267. https://izlik.org/JA85EA56BJ.
JAMA
1.Aktaş M, Çakmak D. A Note on Multivariate Lyapunov-type Inequality. Gazi University Journal of Science. 2015;28:265–267.
MLA
Aktaş, Mustafa, and Devrim Çakmak. “A Note on Multivariate Lyapunov-Type Inequality”. Gazi University Journal of Science, vol. 28, no. 2, June 2015, pp. 265-7, https://izlik.org/JA85EA56BJ.
Vancouver
1.Mustafa Aktaş, Devrim Çakmak. A Note on Multivariate Lyapunov-type Inequality. Gazi University Journal of Science [Internet]. 2015 Jun. 1;28(2):265-7. Available from: https://izlik.org/JA85EA56BJ