On oscillation of first order nonlinear neutral equations (Q1341128)

The authors obtain some sufficient conditions which assure that all solutions of the nonlinear neutral equation (1) oscillate. \[ {d\over dt}[x(t)- c(t) x(t- r)]+ p(t) \prod^ m_{j= 1} [x(t- \tau_ j)]^{\alpha_ j}= 0,\tag{1} \] where \(r> 0\), \(0< \tau_ 1< \tau_ 2<\cdots< \tau_ m\), \(\alpha_ j\geq 0\) \((j= 1,2,\dots, m)\), \(\alpha_ j\in Q\), \(\sum^ m_{j= 1} \alpha_ j= 1\), \(c(\cdot)\in C([t_ 0, +\infty), [0;1])\). If \(c(\cdot)\) and \(p(\cdot)\) are constant then these conditions are also sufficient.