Oscillation of first order nonlinear delay differential equations with periodic coefficients (Q1611435)

Here, the equation \[ x'(t)+ \sum^m_{i=1} p_i(t) \prod^{m_i}_{j=1}|x(t- \tau_{ij})|^{\alpha_{ij}}\text{sign}|x(t)|= 0\tag{1} \] is considered, with \(p_i\in C(\mathbb{R}_+; \mathbb{R}_+)\), \(p_i(t+\omega)= p_i(t)\), \(\tau_{ij}\in (0,+\infty)\), \(\alpha_{ij}\in [0,1]\), \(i= 1,\dots, m\); \(j= 1,\dots, m_i\), \(\omega> 0\), \(\sum^{m_i}_{j=1} \alpha_{ij}= 1\). Sufficient conditions for the oscillation of solutions to equation (1) are established.