Nonlinear Phenomena in Complex Systems, 2006, Vol.9, No.4, pp.380-387

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2006, Vol.9, No.4, pp.380-387

About Stability and Boundedness of Solutions of Certain Fourth Order Differential Equations.
Cemil Tunc

The current paper studies fourth order nonlinear ordinary differential equations of the form

in two cases (i) ; (ii) . In Case (i), the asymptotic stability of the solution x=0 of the equation is studied; in Case (ii), the boundedness and ultimately boundedness of all solutions of the equation are proved. The Lyapunov's second (or direct) method is used as a tool in obtaining the criteria for the asymptotic stability, boundedness and ultimately boundedness of solutions of the equation. Our results revise, improve and include some well-known results established in the relevant literature.
Key words: boundedness, fourth order differential equations, Lyapunov's function, stability

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