Cemil Tunç: On the boundedness of solutions of certain nonlinear vector differential equations of third order, p.291-300

Abstract:

This paper is concerned with the boundedness of all solutions of nonlinear vector differential equations of the form:

$$\stackrel{...}{X}+A(t)F(\stackrel{..}{X})+B(t)G(\stackrel{.}{X})+C(t)H(X)=0.$$

The Lyapunov's second (or direct) method is used as a basic tool in obtaining the criteria for the boundedness of all solutions of the equation.

Key Words: Boundedness, Lyapunov's second method, differential equations of third order.

2000 Mathematics Subject Classification: Primary: 34C11,
Secondary 34A99.

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