Electron. J. Diff. Eqns., Vol. 2006(2006), No. 109, pp. 1-10.

Instability results for certain third order nonlinear vector differential equations

Cemil Tunc, Ercan Tunc

Abstract:
Our goal in this paper is to obtain sufficient conditions for instability of the zero solution to the non-linear vector differential equation
$$ \dddot{X}+F(X,\dot{X})\ddot{X}+G(\dot{X})+H(X)=0. $$
An example illustrates the results obtained.

Submitted July 5, 2006. Published September 11, 2006.
Math Subject Classifications: 34D05, 34D20.
Key Words: Instability, Lyapunov's second (or direct) method; nonlinear differential equations of third order.

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Cemil Tunç
Department of Mathematics
Faculty of Arts and Sciences
Yüzüuncü Yil University, 65080, Van, Turkey
email: cemtunc@yahoo.com
Ercan Tunç
Department of Mathematics
Faculty of Arts and Sciences
Gaziosmanpasa University, 60250, Tokat, Turkey
email: ercantunc72@yahoo.com

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