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

Angelova, D. C.

Arch. Math., Brno 21, 135-146 (1985).

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