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

摘要

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.