versión impresa ISSN 0716-0917
Proyecciones (Antofagasta) vol.30 no.1 Antofagasta 2011
Proyecciones Journal of Mathematics
Vol. 30, N° 1, pp. 43-50, May 2011.
Universidad Católica del Norte
Antofagasta - Chile
On the instability of solutions of an eighth order nonlinear differential equation of retarded type
Yüzüncü Yil University, Van Turkey
In this paper, we give some sufficient conditions on the instability of the zero solution of a kind of eighth order nonlinear differential equations of retarded type by using the Lyapunov direct method. The obtained sufficient conditions improve an existing result in the literature.
Key words : Instability; the Lyapunov direct method; delay differential equation; eighth order.
AMS Classification numbers : 34K20.
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 Bereketoglu, H., On the instability of trivial solutions of a class of eighth-order differential equations. Indian J. Pure Appl. Math. 22, No.3, pp. 199-202, (1991). [ Links ]
 Elsgolts, L. E., Introduction to the theory of differential equations with deviating arguments. Translated from the Russian by Robert J. McLaughlin Holden-Day, Inc., San Francisco, Calif.-London-Amsterdam, (1966). [ Links ]
 Haddock, John R. ; Ko, Y., Liapunov-Razumikhin functions and an instability theorem for autonomous functional-differential equations with finite delay. Second Geoffrey J. Butler Memorial Conference in Differential Equations and Mathematical Biology (Edmonton, AB, 1992). Rocky Mountain J. Math. 25, No. 1, pp. 261-267, (1995). [ Links ]
 Iyase, S. A., Periodic solutions of certain eighth order differential equations. J. Nigerian Math. Soc. 14/15, pp. 31-39, (1995/1996). [ Links ]
 Krasovskii, N. N., On conditions of inversion of A. M. Lyapunov's theorems on instability for stationary systems of differential equations. (Russian) Dokl. Akad. Nauk SSSR (N.S.) 101, pp. 17-20, (1955). [ Links ]
 Tunç, C., Instability of solutions of a certain non-autonomous vector differential equation of eighth-order. Ann. Differential Equations 22, No. 1, pp. 7-12, (2006). [ Links ]
 Tunç, C., Nonexistence of nontrivial periodic solutions to a class of nonlinear differential equations of eighth order. Bull. Malays. Math. Sci. Soc. (2) 32, No. 3, pp. 307-311, (2009). [ Links ]
 Tunç, C.; Tunc, E., An instability theorem for a class of eighth-order differential equations. (Russian) Differ. Uravn. 42 (2006), No. 1, 135-138, 143; translation in Differ. Equ. 42, no. 1, pp. 150-154, (2006). [ Links ]
 Tunç, C., An instability theorem for solutions of a kind of eighth order nonlinear delay differential equations. World Applied Sciences Journal 12 (5) : pp. 619-623, (2011). [ Links ]
Department of Mathematics
Faculty of Arts and Sciences
Yüzüncü Yil University
e-mail : email@example.com
Received : August 2010. Accepted : April 2011