# Stability and boundedness of solutions of nonlinear vector differential equations of third order

## M. O. Omeike

Address: Department of Mathematics, Federal University of Agriculture, Abeokuta, Nigeria

E-mail: moomeike@yahoo.com

Abstract: The paper studies the equation
\begin{equation*}\dddot{X}+\Psi (\dot{X})\ddot{X}+\Phi (X)\dot{X}+cX=P(t) \end{equation*}
in two cases:
(i) $P(t)\equiv 0$,
(ii) $P(t)\ne 0$.
In case (i), the global asymptotic stability of the solution $X=0$ is studied; in case (ii), the boundedness of all solutions is proved.

AMSclassification: primary 34C11; secondary 34D05, 34D20, 34D40.

Keywords: boundedness, stability, Liapunov function, differential equations of third order.

DOI: 10.5817/AM2014-2-101