Sufficient conditions for nonoscillation of neutral equations. (English) Zbl 1090.34599

Ohriska, Jan

Arch. Math., Brno 36, Suppl., 543-548 (2000).

The neutral differential equation \[ \frac {d}{dt}[x(t)+px(t-\tau )]+qx(t-\sigma )=0,\quad t\geq t_0, \] with positive constants \(p\), \(q\), \(\tau \) and \(\sigma \) is considered. Sufficient conditions for the existence of a nonoscillatory solution are presented. The method of investigation (which can be used in investigation of more general equations too) is based on a suitable transformation of the independent variable and on the analysis of corresponding characteristic equation.

Reviewer: Josef Diblík (Brno)

MSC:

34K40

Neutral functional-differential equations

Keywords:

neutral equations; nonoscillatory solutions