Abstract In this paper, we consider the nonlinear fifth
order differential equation
$$x^{(v)}+ax^{(iv)}+b\dddot x+f(\ddot{x})+g(\dot{x})+h(x)=p(t;
x, \dot{x},\ddot{x},\dddot x,x^{(iv)})$$ and we used the
Lyapunov's second method to give sufficient criteria for the zero
solution to be globally asymptotically stable as well as the
uniform boundedness of all solutions with their derivatives.
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