## Services on Demand

## Journal

## Article

## Indicators

## Related links

- Cited by Google
- Similars in SciELO
- Similars in Google

## Share

## Proyecciones (Antofagasta)

##
*Print version* 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 Tunc**

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.

Texto completo sólo en formato PDF

**References**

[1] 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).

[2] 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).

[3] 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).

[4] Iyase, S. A., Periodic solutions of certain eighth order differential equations. J. Nigerian Math. Soc. 14/15, pp. 31-39, (1995/1996).

[5] 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).

[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).

[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).

[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).

[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).

** 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