## 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.

### MSC:

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