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 this paper we shall consider the nonlinear neutral delay differential equations with variable coefficients. Some new sufficient conditions for oscillation of all solutions are obtained. Our results extend and improve some of the well known results in the literature. Some examples are considered to illustrate our main results. The neutral logistic equation with variable coefficients is consid...

In this paper, an oscillation theorem is established for the oscillation of second-order quasilinear neutral differential equation 0 ( )[( ( ) ( ) ( )) ] ( ) ( ( )) 0 r t x t p t x t q t f x t t t                  

In this paper, the author studies the numerical analysis of nonlinear neutral functional differential equations. Functional differential equations (FDEs) arise widely in physics, biology, engineering, medical science, economics and so on. It is meaningful to study the theory and application of numerical methods for FDEs. The result shows gets B-stability, B-consistency and B-convergence results...

Conditions are found upon satisfaction of which the differential equation x(n)(t)− λx(n)(t− σ) + f(t, x(g(t))) = 0 has solutions which are asymptotically equivalent to the solutions of the equation x(n)(t)− λx(n)(t− σ) = 0. § 0. Introduction We consider the neutral functional differential equation x(n)(t)− λx(n)(t− σ) + f(t, x(g(t))) = 0 (A) under the assumptions that (i) n ≥ 1 is an integer; λ...

In this article, we consider a model for the spread of certain infectious disease governed by a delay integro-differential equation. We obtain the existence and the uniqueness of a positive periodic solution, by using Perov’s fixed point theorem in generalized metric spaces.

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...

This paper presents a numerical matrix method based on Bernstein polynomials (BPs) for approximate the solution of a system of m-th order nonlinear Volterra integro-differential equations under initial conditions. The approach is based on operational matrices of BPs. Using the collocation points,this approach reduces the systems of Volterra integro-differential equations associated with the giv...

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

in this paper, differential transform method (dtm) is described and is applied to solve systems of nonlinear ordinary differential equations which is arising in hiv infections of cell. intervals of validity of the solution will be extended by using pade approximation. the results also will be compared with those results obtained by runge-kutta method. the technique is described and is illustrat...