On the instability of certain sixth-order nonlinear differential equations

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].