Oscillations of systems of neutral differential equations. (English) Zbl 0723.34057

Summary: We obtain sufficient conditions for the oscillation of all solutions of the system of neutral delay differential equations \[ \frac{d}{dt}[x(t)- Px(t-\tau)]+\sum^{m}_{k=1}Q_ kx(t-\sigma_ k)=0, \] where P is an \(n\times n\) diagonal matrix with diagonal entries \(p_ 1,p_ 2,...,p_ n\) such that \(0\leq p_ i\leq 1\) for \(i=1,2,...,n\), the delays \(\tau\) and \(\sigma_ k\) for \(k=1,2,...,m\) are nonnegative and for each \(k=1,2,...,n\) the entries \(q_{ij}^{(k)}\) of the \(n\times n\) matrix \(Q_ k\) are real numbers. Our results can be extended to systems with the \(Q_ k's\) continuous \(n\times n\) matrices.


34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument)
34K40 Neutral functional-differential equations