Oscillatory Mixed Differential Systems

In this work are obtained some criteria which guarantee the oscillatory behavior of the differential system of mixed type \[x'(t)=\int_{-1}^0 d[\nu(\theta)] x(t-r(\theta)) + \int_{-1}^0 d[\eta(\theta)]x(t+\tau(\theta))\] where \(x(t)\in\mathbb{R}^n\), \(r(\theta)\) and \(\tau(\theta)\) are real \(n\times n\) matrix valued functions of bounded variation on \([-1,0]\).