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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.30 no.1 Antofagasta  2011

http://dx.doi.org/10.4067/S0716-09172011000100004 

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


Cemil Tunç

Yüzüncü Yil University, Van Turkey


Correspondencia a:


Abstract

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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References

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[6] 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 ]

[7] 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 ]

[8] 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 ]

[9] 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 ]


Cemil Tunç
Department of Mathematics
Faculty of Arts and Sciences
Yüzüncü Yil University
65080, VAN-TURKEY
e-mail : cemtunc@yahoo.com


Received : August 2010. Accepted : April 2011