×

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.

MSC:

34K11 Oscillation theory of functional-differential equations
34K40 Neutral functional-differential equations
34K25 Asymptotic theory of functional-differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chen, Ming-Po; Yu, J. S.; Huang, L. H., Oscillation of first order neutral differential equations with variable coefficients, J. Math. Anal. Appl., 185, 288-301 (1994) · Zbl 0807.34081
[2] Das, P.; Misra, N., A necessary and sufficient condition for the solution of a functional differential equation to be oscillatory or tend to zero, J. Math. Anal. Appl., 204, 78-87 (1997) · Zbl 0874.34058
[3] Gyori, I.; Ladas, G., Oscillation Theory of Delay-Differential Equations with Applications (1991), Clarendon: Clarendon Oxford · Zbl 0780.34048
[4] Kulenovic, M. R.S.; Ladas, G.; Meimaridou, A., Necessary and sufficient conditions for oscillation of neutral differential equations, J. Austral. Math. Soc. Ser. B, 28, 362-375 (1987) · Zbl 0616.34064
[5] Lalli, B. S.; Zhang, B., Oscillation of first order neutral differential equations, Appl. Anal., 39, 265-274 (1990) · Zbl 0725.34074
[6] Parhi, N.; Rath, R. N., On oscillation criteria for a forced neutral differential equation, Bull. Inst. Math. Acad. Sinica, 28, 59-70 (2000) · Zbl 0961.34059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.