By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order Emden-Fowler delay dynamic equations rxΔ Δ t p t x τ t 0 on a time scale T; here γ is a quotient of odd positive integers with r and p as real-valued positive rd-continuous functions defined on T. Our results in this paper not only extend the results given in Agarwal et al. 2005 , Akin-...

We present new oscillation criteria for the second order nonlinear neutral delay differential equation ( a (t) (y (t)+ p (t) y (t − τ))′)′ + q (t) |y (σ (t))|α−1 y (σ (t)) = 0, where t ≥ t0, τ, and α are positive constants and the functions p, q, a, σ ∈ C ([t0,∞) ,R) . Our results generalize and improve some known results for oscillation of second order neutral delay differential equations. Our...

By means of Riccati transformation technique, we establish some new oscillation criteria for the second-order nonlinear delay dynamic equations r t xΔ t γ Δ p t f x τ t 0 on a time scale T; here γ > 0 is a quotient of odd positive integers with r and p real-valued positive rdcontinuous functions defined on T. Our results not only extend some results established by Hassan in 2008 but also unify ...

A kind of fourth-order delay differential equation is considered. Firstly, the linear stability is investigated by analyzing the associated characteristic equation. It is found that there are stability switches for time delay and Hopf bifurcations when time delay cross through some critical values. Then the direction and stability of the Hopf bifurcation are determined, using the normal form me...

We study the onset of sustained oscillations in a classical state-dependent delay (SDD) differential equation inspired by control theory. Owing to the large delays considered, the Hopf bifurcation is singular and the oscillations rapidly acquire a sawtooth profile past the instability threshold. Using asymptotic techniques, we explicitly capture the gradual change from nearly sinusoidal to sawt...

Some sufficient conditions for oscillation of a first order nonautonomuous delay differential equation with several positive and negative coefficients are obtained.

Neutral differential equations find numerous applications in natural science and technology. For instance, they are frequently used for the study of distributed networks containing lossless transmission lines; see Hale 1 . In recent years, many studies have been made on the oscillatory behavior of solutions of neutral delay differential equations, and we refer to the recent papers 2–23 and the ...

The main result of this paper is that the oscillation and nonoscillation properties of a nonlinear impulsive delay differential equation are equivalent respectively to the oscillation and nonoscillation of a corresponding nonlinear delay differential equation without impulse effects. An explicit necessary and sufficient condition for the oscillation of a nonlinear impulsive delay differential e...