Oscillation properties of solutions to functional-differential equations (Q1363980)

The author considers the differential equation with delay \[ u^{(n)} (t) + F(u)(t) = 0,\tag{1} \] where \( F:C^{n-1}(\mathbb{R}_+,\mathbb{R})\to L_{\text{loc}}(\mathbb{R}_+,\mathbb{R}) \) is a continuous operator. New sufficient, necessary and sufficient conditions are given for the oscillation of all regular solutions to (1).