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


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