Electron. J. Diff. Eqns., Vol. 2004(2004), No. 117, pp. 1-6.

On the instability of certain sixth-order nonlinear differential equations

Cemil Tunc

In this paper, we give an instability criteria for the nonlinear sixth-order vector differential equation
 X^{(6)} + AX^{(5)} +B(t)\Phi (X,\dot {X},\ddot {X},
 X^{(3)},X^{(4)},X^{(5)})X^{(4)} +
 C(t)\Psi (\ddot {X}),X^{(3)}\cr
 +D(t)\Omega (X,\dot {X},\ddot {X},X^{(3)},X^{(4)},X^{(5)})
 \ddot {X}+E(t)G(\dot {X})+H(X) = 0\,.
The result extends and includes earlier results [6,16,20].

Submitted July 13, 2004. Published October 7, 2004.
Math Subject Classifications: 34D05, 34D20.
Key Words: Nonlinear differential equations of sixth order; instability; Lyapunov function.

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

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