Invariant and attracting sets of impulsive delay difference equations with continuous variables

AbstractThe aim of this paper is to study the invariant and attracting sets of impulsive delay difference equations with continuous variables. Some criteria for the invariant and attracting sets are obtained by using the decomposition approach and delay difference inequalities with impulsive initial conditions

Oscillatory criteria for Third-Order difference equation with impulses

AbstractIn this paper, we investigate the oscillation of Third-order difference equation with impulses. Some sufficient conditions for the oscillatory behavior of the solutions of Third-order impulsive difference equations are obtained

On the behaviour of solutions of neutral impulsive difference equations of second order

The work embodied in this paper is the study of oscillation properties of a class of second order neutral impulsive difference equations with constant coefficients. In addition, an effort is made here to apply constant coefficient results to nonlinear impulsive difference equations with variable coefficients

Oscillation of third order Impulsive Differential Equations with delay

This paper deals with the oscillation of third order impulsive differential equations with delay. The results of this paper improve and extend some results for the differential equations without impulses. Some examples are givento illustrate the main results

Oscillation of θ-methods for the Lasota-Wazewska model

The aim of this paper is to discuss the oscillation of numerical solutions for the Lasota-Wazewska model. Using two θ-methods (the linear θ-method and the one-leg θ-method), some conditions under which the numerical solutions oscillate are obtained for different range of θ. Furthermore, it is shown that every non-oscillatory numerical solution tends to the fixed point of the original continuous equation. Numerical examples are given

On the Oscillation of Impulsive Neutral First-order Differential Equations with Variable Arguments

Throughout the article, we study the oscillation of a general class of first-order neutral differential equations in presence of variable delays under the effect of impulses. Due to its importance in applications, there are many papers concerning with the property of oscillation and non-oscillation of neutral delay differential equations. Although, a lot of works are concerning with the oscillation of neutral delay differential equations without impulse or impulsive neutral with constant delays, however few papers dealt with the impulsive neutral and those with variable delays. In this paper, we establish sufficient conditions of certain neutral equations with variable delay arguments. New oscillation criteria are deduced. Our results are based on using equivalence transformation and two useful lemmas to prove the obtained criteria. The results of this paper improve those of [20] by adding several non-linear delay functions to the equations instead of having one delay term. Where it is assumed that the two variable delays satisfying a Lipschitz condition. Moreover we discuss more general non-linear delay functions comparing with those used in [14]. Our results improve and extend some recent results in the literature. An illustrative example is given

Global exponential stability for coupled systems of neutral delay differential equations

In this paper, a novel class of neutral delay differential equations (NDDEs) is presented. By using the Razumikhin method and Kirchhoff's matrix tree theorem in graph theory, the global exponential stability for such NDDEs is investigated. By constructing an appropriate Lyapunov function, two different kinds of sufficient criteria which ensure the global exponential stability of NDDEs are derived in the form of Lyapunov functions and coefficients of NDDEs, respectively. A numerical example is provided to demonstrate the effectiveness of the theoretical results