Analytical and numerical treatment of oscillatory mixed differential equations with differentiable delays and advances

In this work, we study the oscillatory behaviour of the differential equation of mixed type x′(t)=∫−10x(t−r(θ))dν(θ)+∫−10x(t+τ(θ))dη(θ) with delays r(θ) and advances τ(θ), both differentiable. Some analytical and numerical criteria are obtained in order to guarantee that all solutions are oscillatory.