In this study, new asymptotic properties of positive solutions the even-order neutral delay differential equation with noncanonical operator are established. The an iterative nature, which allows it to be applied several times. Using these properties, we obtain criteria exclude a class from studied equation, using comparison principles.

Some sufficient conditions are established for the oscillation of second-order neutral differential equation x t p t x τ t ′′ q t f x σ t 0, t ≥ t0, where 0 ≤ p t ≤ p0 < ∞. The results complement and improve those of Grammatikopoulos et al. Ladas, A. Meimaridou, Oscillation of second-order neutral delay differential equations, Rat. Mat. 1 1985 , Grace and Lalli 1987 , Ruan 1993 , H. J. Li 1996 ...

Some sufficient conditions are established for the oscillation of second-order neutral differential equation x t p t x τ t ′′ q t f x σ t 0, t ≥ t0, where 0 ≤ p t ≤ p0 < ∞. The results complement and improve those of Grammatikopoulos et al. Ladas, A. Meimaridou, Oscillation of second-order neutral delay differential equations, Rat. Mat. 1 1985 , Grace and Lalli 1987 , Ruan 1993 , H. J. Li 1996 ...

In the paper, we offer such generalization of a lemma due to Philos (and partially Staikos), that yields many applications in the oscillation theory. We present its disposal in the comparison theory and we establish new oscillation criteria for n−th order delay differential equation (E) ` r(t) ˆ x ′(t) ̃ γ ́(n−1) + q(t)xγ(τ (t)) = 0. The presented technique essentially simplifies the examination...

We propose a new method for constructing exact solutions to nonlinear delay reaction–diffusion equations of the form ut = kuxx + F (u,w), where u = u(x, t), w = u(x, t−τ), and τ is the delay time. The method is based on searching for solutions in the form u = ∑N n=1 ξn(x)ηn(t), where the functions ξn(x) and ηn(t) are determined from additional functional constraints (which are difference or fun...

In this article, we establish some new criteria for the oscillation of fourth order nonlinear delay differential equations of the form x(t) + p(t)x(t) + q(t)f(x(g(t))) = 0 provided that the second order equation z(t) + p(t)z(t) = 0 is nonoscillatiory or oscillatory. This equation with g(t) = t is considered in [8] and some oscillation criteria for this equation via certain energy functions are ...

We have given some results regarding the behavior of solutions for first order linear impulsive neutral delay differential equations with constant coefficients. These were obtained using two different real roots corresponding characteristic equation. Finally, examples are equations.

This paper deals with the singularly perturbed boundary value problem for a linear second order differential-difference equation of the convection-diffusion type with small delay parameter. A fourth order finite difference method is developed for solving singularly perturbed differential difference equations. To handle the delay argument, we construct a special type of mesh, so that the term co...

A model for a 1–dimensional delayed random walk is developed by generalizing the Ehrenfest model of a discrete random walk evolving on a quadratic, or harmonic, potential to the case of non–zero delay. The Fokker–Planck equation derived from this delayed random walk (DRW) is identical to that obtained starting from the delayed Langevin equation, i.e. a first–order stochastic delay differential ...