Nonoscillation and oscillation of first order neutral equations with variable coefficients (Q1323077)

The neutral equations \[ \left[x(t)- \sum^ k_{i=1} c_ i(t) x(t- \nu_ i(t))\right]'+ Q(t) x(t- \sigma)= 0,\quad t\geq t_ 0, \] are considered, where \(\sigma>0\), \(Q(t)>0\), \(c_ i(t)> 0\), \(0< \nu_ 0< \nu_ i(t)\leq \nu\) when \(t\in [t_ 0,+\infty)\) \((i= 1,\dots, k)\). Sufficient conditions are given for the present equation to have nonoscillatory solutions (every of its regular solution to be oscillatory).