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Sufficient conditions for nonoscillation of neutral equations. (English) Zbl 1090.34599
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.
MSC:
34K40 Neutral functional-differential equations
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