TY - JOUR AU - OMEIKE, M. O. AU - ADEYANJU, A. A. AU - ADAMS, D. O. PY - 2018/08/31 Y2 - 2024/03/29 TI - STABILITY AND BOUNDEDNESS OF SOLUTIONS OF CERTAIN VECTOR DELAY DIFFERENTIA EQUATIONS JF - Journal of the Nigerian Mathematical Society JA - JNMS VL - 37 IS - 2 SE - Articles DO - UR - https://ojs.ictp.it/jnms/index.php/jnms/article/view/331 SP - 77-87 AB - In this paper, certain class of second-order vector delay differential equation of the form<p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">$$\ddot{X} + A \dot{X} + H(X(t -r(t))) = P(t,X,\dot{X})$$</p><p style="-qt-block-indent: 0; text-indent: 0px; margin: 0px;">is considered where $ X \in \mathbb{R}^n$, $0 \leq r(t) \leq \gamma $ and $A$ is a real constant, symmetric positive definite $n \times n$ matrix. By using the second method of Lyapunov and Lyapunov-Krasovskii's funtion we established sufficient conditions for the asymptotic stability of the zero solution when $P(t, X, \dot{X}) = 0$ and boundedness of all solutions when $P(t, X, \dot{X}) eq 0$. The results obtained here are generalizations of some of the results obtained for $\mathbb{R}^1.$</p> ER -