Comparison of oscillation of higher order delay differential equations (Q675960)

The authors consider the \(n\)-th order delay differential equations of the form \[ x^{(n)}(t)+ (-1)^{n+1} \sum_{i=0}^k Q_i(t)f_i(x(t-\tau_i))=0.\tag{1} \] Using an associated linear differential equation with constant coefficients there are proved sufficient conditions for the oscillation of all solutions of (1) for \(n\) odd and all bounded solutions of (1) for \(n\) even.