STABILITY AND BOUNDEDNESS OF SOLUTIONS OF CERTAIN VECTOR DELAY DIFFERENTIA EQUATIONS

M. O. OMEIKE, A. A. ADEYANJU, D. O. ADAMS

Abstract


In this paper, certain class of second-order vector delay differential equation of the form

$$\ddot{X} + A \dot{X} + H(X(t -r(t))) = P(t,X,\dot{X})$$

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 $P(t, X, \dot{X}) \neq 0$. The results obtained here are generalizations of some of the results obtained for $\mathbb{R}^1.$


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References


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