Multiple Integral Average Conditions for Oscillation of Delay Differential Equations

Oscillation of Volterra Integral Equations and Forced Functional Differential Equations

Survey of Oscillation Criteria for First Order Delay Differential Equations

In this paper, we discuss the oscillatory behavior of first order delay differential equations of the form: y′(t) + p(t)y(τ(t)) = 0, t ≥ T, where p and T are continuous functions defined on [T,∞), p(t) > 0, τ(t) < t for t ≥ T, τ(t) is nondecreasing and lim t→∞ τ(t) = ∞. We present best possible conditions for the oscillation of all solutions for this equation.

Oscillation Criteria for Nonlinear Delay Differential Equations of Second Order∗

We prove oscillation theorems for the nonlinear delay differential equation

Necessary and Sufficient Conditions for Oscillation of Neutral Delay Differential Equations

In this article, we concerned with oscillation of the neutral delay differential equation [x(t) − px(t − τ)]′ + qx(t − σ) = 0 with constant coefficients. By constructing several suitable auxiliary functions, we obtained some necessary and sufficient conditions for oscillation of all the solutions of the aforementioned equation for the cases 0 < p < 1 and p > 1.

Integral Operators and Delay Differential Equations

The monodromy operator of a linear delay differential equation with periodic coefficients is formulated as an integral operator. The kernel of this operator includes a factor formed from the fundamental solution of the linear delay differential equation. Although the properties of the fundamental solutions are known, in general there is no closed form for the fundamental solution. This paper de...