Lyapunov-type inequalities for higher order difference equations with anti-periodic boundary conditions

  • Erjing Wang College of Math. & Info.Sci., Hebei Normal University, China
  • Qiaoluan Li College of Math. & Info.Sci., Hebei Normal University, China
Keywords: Difference equation, Anti-periodic boundary conditions, Lyapunov-type inequalities

Abstract

In this paper, some new Lyapunov-type inequalities for higher order difference equations with anti-periodic boundary conditions are established. The obtained results are used to obtain the lower bounds for the eigenvalues of corresponding equations.

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References

D. Cakmak, Lyapunov-type integral inequalities for certain higher order differential equations, Appl. Math. Comput. 216 (2010) 368-373.

S. S. Cheng, A discrete analogue of the inequality of Lyapunov, Hokkaido Math. J. 12 (1983) 105-112.

X. He, X. H. Tang, Lyapunov-type inequatlities for even order differential equations, Commun Pure Appl. Anal. 11 (2) (2012) 465-473.

A. M. Liapunov, Probleme general de la stabilite du mouvement, Ann. Fac. Sci. Univ. Toulouse, 2 (1907) 203-407.

X. G. Liu, M. L. Tang, Lyapunov- type inequality for higher order difference equations, Appl. Math. Comput. 232 (2014) 666-669.

Y. Y. Wang, Lyapunov-type inequalities for certain higher order differential equations with anti-periodic boundary conditions, Appl. Math. Lett. 25 (2012) 2375-2380.

Y. Wang, Y. M. Shi, Eigenvalues of second-order difference equations with periodic and antiperiodic boundary conditions, J. Math. Anal. Appl. 309 (2005) 56-69.

X. Yang, On Lyapunov-type inequality for certain higher-order differential equations, Appl. Math. Comput. 134 (2003) 307-317.

X. Yang, K. Lo, Lyapunov-type inequality for a class of even-order differential equations, Appl. Math. Comput. 215 (2010) 3884-3890.

Q. M. Zhang, X. H. Tang, Lyapunov-type inequalities for even order difference equations, Appl. Math. Lett. 25 (2012) 1830-1834.

Published
2018-06-13
How to Cite
Wang, E., & Li, Q. (2018). Lyapunov-type inequalities for higher order difference equations with anti-periodic boundary conditions. Journal of Progressive Research in Mathematics, 13(3), 2316-2321. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/1545
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Articles