A Note on Multivariate Lyapunov-type Inequality
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.
___
- [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.
- Yayın Aralığı: 4
- Başlangıç: 1988
- Yayıncı: Gazi Üniversitesi, Fen Bilimleri Enstitüsü