Spectral bounds and oscillations of a differential-difference system of neutral type (Q1592715)

The authors consider the linear delay differential-difference system of neutral type having the form \[ d/dt\bigl[x(t)- Bx(t-\tau)\bigr]= Ax(t-r) \tag{1} \] with \(x(t)\in\mathbb{R}^n\) and \(A,B\) are nonzero matrices in \(\mathbb{R}^{n \times n}\). Moreover, \(\tau\) and \(r\) are positive reals. Sufficient conditions implying that all solutions to (1) are oscillatory on the interval \([-R,+ \infty)\) \((R=\max \{\tau,r\})\) are the main object of the paper. Two examples illustrating the obtained results are presented.