ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

We present here the ultimate boundedness of solutions of some nonlinear non-homogeneous vector differential equation of the third order, by means of the Lyapunov second method. We provide, in simple form, sufficient conditions which ensure ultimate boundedness of solutions of equations of the form $$\stackrel{...}{X}+\phi(\dot{X})\ddot{X}+G(\dot{X})+H(X)=P(t,X,\dot{X},\ddot{X}).$$ Results obtained generalize, improve and include the results obtained by previous authors.