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 ...

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...

In this paper, we study the existence of almost periodic solutions of neutral differential difference equations with piecewise constant arguments via difference equation methods.

In the last few years there has been much interest in studying the oscillatory behaviour of solutions of partial differential equations with deviating arguments. We refer the reader to Mishev & Bainov [1], [2], Yoshida [3], Georgiou & Kreith [4] and Cui [5]. However, only the papers [1] and [5] considered the oscillation for parabolic differential equations of neutral type. The purpose of this ...

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 ...

This paper studies the existence and uniqueness of a mild solution, satisfying Caratheodory conditions, for a neutral stochastic partial functional differential equation with infinite delays and Poisson jumps.

This article mainly considers the linear neutral delay-differential systems with a single delay. Using the characteristic equation of the system, new simple delay-independent asymptotic and exponential stability criteria are derived in terms of the matrix measure, the spectral norm and the spectral radius of the corresponding matrices. Numerical examples demonstrate that our criteria are less c...