Oscillation criteria for forced first order neutral differential equations with variable coefficients. (English) Zbl 0982.34057

The authors discuss the forced first-order neutral differential equation \[ (y(t)-p(t)y(t-\tau))'+\delta Q(t)G(y(t-\sigma))=f(t), \] with \(\delta=\pm 1\), \(p(t)\in C([0, \infty), \mathbb{R})\) is considered in various ranges. Conditions are obtained so that every solution to the equation is oscillatory or tends to zero or to \(\pm \infty\) as \(t\rightarrow \infty\). For \(\delta =1\), necessary and sufficient conditions are also given.


34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
34K25 Asymptotic theory of functional-differential equations
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