Journal ArticleDOI
On oscillations of some retarded differential equations
O. Arino,G. Ladas,Y. G. Sficas +2 more
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In this paper, the authors obtained sufficient conditions for the oscillation of delay differential equations with oscillating coefficients, where p, q, $\tau $, and $\sigma $ are positive constants.Abstract:
Consider the delay differential equation \[ (*)\quad y'(t) + py(t - \tau ) - qy(t - \sigma ) = 0\] where p, q, $\tau $, and $\sigma $ are positive constants.THEOREM. Assume that$\sigma \leqq \tau $, $q 1$. Then every solution of$(*)$oscillates.The above result was extended to equations with several delays.Finally we obtained sufficient conditions for the oscillation of delay differential equations with oscillating coefficients.read more
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Journal ArticleDOI
Oscillation criteria for delay equations
TL;DR: In this article, the oscillatory behavior of first-order delay differential equations was studied and it was shown that τ(t) is non-decreasing, τ (t) < t for t ≥ t 0 and limt→∞ τ(τ) = ∞.
Journal ArticleDOI
Oscillation Tests for Delay Equations
J. Jaros,Ioannis P. Stavroulakis +1 more
TL;DR: In this article, the oscillatory behavior of first-order delay differential equations is studied, where p, τ ∈ C([T, ∞),R+), R+ = [0,∞], τ(t) is non-decreasing, τ (t) < t for t ≥ T and limt→∞ τ(τ) = ∞.
Journal ArticleDOI
Oscillation in Differential Equations with Positive and Negative Coefficients
TL;DR: In this article, sufficient conditions for the oscillation of all solutions of the linear delay differential equation with positive and negative coefficients where extensions to neutral differential equations and some applications to the global asymptotic stability of the trivial solution are also given.
Journal ArticleDOI
Oscillation criteria for first-order delay equations
TL;DR: In this article, the oscillatory behaviour of first-order delay differential equations of the form is studied, where all solutions of equation (1) oscillate in several cases in which the condition holds.
Journal ArticleDOI
Neutral delay differential equations with positive and negative coefficients
K. Farrell,E. A. Grove,G. Ladas +2 more
TL;DR: In this article, the authors studied the asymptotic behavior of nonoscillatory solutions of the neutral delay differential equation and obtained sufficient conditions for the oscillation of all solutions, all bounded solutions, and all unbounded solutions.