Geodesic
On the instability of certain sixth-order nonlinear differential equations
Electronic journal of differential equations, Tome 2004 (2004)
In this paper, we give an instability criteria for the nonlinear sixth-order vector differential equation

$\displaylines{ X^{(6)} + AX^{(5)} +B(t)\Phi (X,\dot {X},\ddot {X}, X^{(3)},X^{(4)},X^{(5)})X^{(4)} + C(t)\Psi (\ddot {X}),X^{(3)}\cr +D(t)\Omega (X,\dot {X},\ddot {X},X^{(3)},X^{(4)},X^{(5)}) \ddot {X}+E(t)G(\dot {X})+H(X) = 0\,. }$

The result extends and includes earlier results [6,16,20].
Classification : 34D05, 34D20
Keywords: nonlinear differential equations of sixth order, instability, Lyapunov function 
@article{EJDE_2004__2004__a24,
     author = {Tunc,  Cemil},
     title = {On the instability of certain sixth-order nonlinear differential equations},
     journal = {Electronic journal of differential equations},
     year = {2004},
     volume = {2004},
     zbl = {1075.34047},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a24/}
}
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Tunc,  Cemil. On the instability of certain sixth-order nonlinear differential equations. Electronic journal of differential equations, Tome 2004 (2004). http://geodesic.mathdoc.fr/item/EJDE_2004__2004__a24/