Electron. J. Diff. Eqns., Vol. 2005(2005), No. 51, pp. 1-6.

Instability of solutions of certain nonlinear vector differential equations of third order

Ercan Tunc

Abstract:
In this paper, study the system of differential equations
$$ \dddot{X}+F(\dot{X})\ddot{X}+G(X)\dot{X} +H(X,\dot{X},\ddot{X})=0\,. $$
We find sufficient conditions for the zero solution to be unstable, and to be the only periodic solution.

Submitted March 14, 2005. Published May 11, 2005.
Math Subject Classifications: 34D20, 34C25, 34A34.
Key Words: Nonlinear differential equations of third order; instability; periodic solution; Lyapunov's method.

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Ercan Tunc
Faculty of Arts and Sciences
Department of Mathematics
Gaziosmanpas a University
60240, Tokat, Turkey
email: ercantunc72@yahoo.com

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