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A Note on Multivariate Lyapunov-type Inequality

Year 2015, Volume: 28 Issue: 2, 265 - 267, 22.06.2015

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.

References

  • [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] M. F. Aktaş, On the multivariate Lyapunov inequalities, Appl. Math. Comput., 232 (2014), 784- 786.
  • [3] G. A. Anastassiou, Multivariate Lyapunov inequalities, Appl. Math. Letters, 24 (2011), 2167-2171.
  • [4] A. Canada, J. A. Montero, S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal., 237 (2006), 176-193.
  • [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] D. Çakmak, Lyapunov-type integral inequalities for certain higher order differential equations, Appl. Math. Comput., 216 (2010), 368-373.
  • [7] A. M. Liapunov, Probléme général de la stabilité du mouvement, Ann. Fac. Sci. Univ. Toulouse, 2 (1907), 203-407.
  • [8] W. Rudin, Real and Complex Analysis, McGrawHill, New York, 1970.
  • [9] X. Yang, K. Lo, Lyapunov-type inequality for a class of even-order differential equations, Appl. Math. Comput., 215 (2010), 3884-3890.
Year 2015, Volume: 28 Issue: 2, 265 - 267, 22.06.2015

Abstract

References

  • [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] M. F. Aktaş, On the multivariate Lyapunov inequalities, Appl. Math. Comput., 232 (2014), 784- 786.
  • [3] G. A. Anastassiou, Multivariate Lyapunov inequalities, Appl. Math. Letters, 24 (2011), 2167-2171.
  • [4] A. Canada, J. A. Montero, S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal., 237 (2006), 176-193.
  • [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] D. Çakmak, Lyapunov-type integral inequalities for certain higher order differential equations, Appl. Math. Comput., 216 (2010), 368-373.
  • [7] A. M. Liapunov, Probléme général de la stabilité du mouvement, Ann. Fac. Sci. Univ. Toulouse, 2 (1907), 203-407.
  • [8] W. Rudin, Real and Complex Analysis, McGrawHill, New York, 1970.
  • [9] X. Yang, K. Lo, Lyapunov-type inequality for a class of even-order differential equations, Appl. Math. Comput., 215 (2010), 3884-3890.
There are 9 citations in total.

Details

Primary Language English
Journal Section Mathematics
Authors

Mustafa Aktaş

Devrim Çakmak

Publication Date June 22, 2015
Published in Issue Year 2015 Volume: 28 Issue: 2

Cite

APA Aktaş, M., & Çakmak, D. (2015). A Note on Multivariate Lyapunov-type Inequality. Gazi University Journal of Science, 28(2), 265-267.
AMA Aktaş M, Çakmak D. A Note on Multivariate Lyapunov-type Inequality. Gazi University Journal of Science. June 2015;28(2):265-267.
Chicago Aktaş, Mustafa, and Devrim Çakmak. “A Note on Multivariate Lyapunov-Type Inequality”. Gazi University Journal of Science 28, no. 2 (June 2015): 265-67.
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 M. Aktaş and D. Çakmak, “A Note on Multivariate Lyapunov-type Inequality”, Gazi University Journal of Science, vol. 28, no. 2, pp. 265–267, 2015.
ISNAD Aktaş, Mustafa - Çakmak, Devrim. “A Note on Multivariate Lyapunov-Type Inequality”. Gazi University Journal of Science 28/2 (June 2015), 265-267.
JAMA 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, 2015, pp. 265-7.
Vancouver Aktaş M, Çakmak D. A Note on Multivariate Lyapunov-type Inequality. Gazi University Journal of Science. 2015;28(2):265-7.