Oscillations of equations with piecewise constant mixed arguments. (English) Zbl 0711.34083

Differential equations and applications, Proc. Int. Conf., Columbus/OH (USA) 1988, Vol. II, 64-69 (1989).
Summary: [For the entire collection see Zbl 0707.00015.]
We obtain necessary and sufficient conditions for the oscillation of all solutions of the differential equation with piecewise constant mixed arguments \[ \dot x(t)+px(t)+\sum^{m}_{j=-\ell}q_ jx([t+j])=0,\quad t\geq 0, \] where [\(\cdot]\) denotes the greatest integer function, \(\ell,m\in \{0,1,2,...\}\) and \(p,q_ j\in {\mathbb{R}}\) for \(j=-\ell,...,m\).


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




Zbl 0707.00015