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.

Keywords: Boundedness; Lyapunov function; nonlinear fifth order differential equations; stability.

MSC: 34A34, 34D20, 34D23, 34D99

Pages:  257$-$268     

Volume  61 ,  Issue  4 ,  2009