## Quickly, moderately and slowly oscillatory solutions of a second order functional differential equation.(English)Zbl 0586.34059

This paper considers the behaviour of quickly, moderately and slowly oscillatory solutions of the equation $$(r(t)y'(t))'+f(t,y(\Delta (t,y(t))))=Q(t),$$ $$t\geq t_ o\in {\mathbb{R}}^ 1$$ in the cases when $$\lim \inf_{t\to \infty}r(t)>0$$ and $$\lim \inf_{t\to \infty}r(t)=0$$ and when the deviation $$\Delta$$ (t,u) depends on the unknown function and may be of a retarded, advanced or mixed type.

### MSC:

 34K99 Functional-differential equations (including equations with delayed, advanced or state-dependent argument) 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations

### Keywords:

autonomous retarded systems; oscillatory solutions
Full Text: