Asymptotic behavior of solutions of nonlinear neutral differential equations with impulses

This paper is concerned with a nonlinear neutral differential equations with impulses of the form

(*)     

Asymptotic behavior of solutions of second-order nonlinear delay differential equations with impulses

This paper is concerned with second-order nonlinear delay differential equations with impulses of the form

     

Asymptotic behavior of solutions for nonlinear delay differential equation with impulses

This paper studies the asymptotic behavior of solutions of the nonlinear delay differential equation with impulses

     

Asymptotic behavior of delay differential equations with instantaneously terms

This paper deals with scalar delay differential equation with instantaneously term

     

Asymptotic behavior of certain delay differential equations with forcing term

We study the asymptotic behavior of solutions of the following forced delay differential equation:

Some sufficient conditions that guarantee every solution of the equation to converge to zero are obtained. The results obtained are applied to some well-known delay differential ecological equations with forcing term.     

Asymptotic behavior of solutions of neutral differential equations with positive and negative coefficients

Sufficient conditions are established for the asymptotic behavior of solutions of neutral differential equations with positive and negative coefficients

     

Asymptotic behavior of solutions of second-order nonlinear impulsive differential equations

In this work, the asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses is investigated. By impulsive differential inequality and Riccati transformation, sufficient conditions of asymptotic behavior of all solutions of second-order nonlinear ordinary differential equations with impulses are obtained. An example is also inserted to illustrate the impulsive effect.     

Oscillation properties of nonlinear impulsive delay differential equations and applications to population models

Comparison theorem and explicit sufficient conditions are obtained for oscillation and nonoscillation of solutions of nonlinear impulsive delay differential equations which can be utilized to population dynamic models. Our results in this paper generalize and improve several known results.     

Global existence results for impulsive functional differential equations

In this paper, we investigate the existence of solutions of impulsive delay differential equation

     

Asymptotic behavior of solutions to abstract functional differential equations

In this paper, a new approach is provided to study the asymptotic behavior of functions. A Tauberian theorem is improved and applied to describe the asymptotic behavior of abstract functional differential equations of the form

     

Existence of positive solutions of nonlinear fractional delay differential equations

This paper investigates the existence and uniqueness of positive solutions for a class of nonlinear fractional delay differential equations. Using a nonlinear alternative of Leray-Schauder type, we show the existence of positive solutions for the equations in question.     

Asymptotic behavior and oscillation of functional differential equations

Asymptotic relations between the solutions of a linear autonomous functional differential equation and the solutions of the corresponding perturbed equation are established. In the scalar case, it is shown that the existence of a nonoscillatory solution of the perturbed equation often implies the existence of a real eigenvalue of the limiting equation. The proofs are based on a recent Perron type theorem for functional differential equations.     

Asymptotic behavior results for nonlinear neutral delay difference equations

This paper is concerned with the nonlinear neutral delay difference equation

(∗)     

Asymptotic behavior of bounded solutions for a system of neutral functional differential equations

Consider the system of neutral functional differential equations

     

Asymptotic behavior and stability of second order neutral delay differential equations

We study the asymptotic behavior of a class of second order neutral delay differential equations by both a spectral projection method and an ordinary differential equation method approach. We discuss the relation of these two methods and illustrate some features using examples. Furthermore, a fixed point method is introduced as a third approach to study the asymptotic behavior. We conclude the paper with an application to a mechanical model of turning processes.     

Existence of positive periodic solutions of impulsive functional differential equations with two parameters

In this paper, we employ a well-known fixed-point index theorem to study the existence and non-existence of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. Several existence and non-existence results are established.     

Asymptotic behavior of a third-order nonlinear differential equation

Consider the third-order nonlinear differential equation

x?+ψ(x,x′)x″+f(x,x′)=p(t),     

Uniform stability theorems for delay differential equations with impulses

In the paper, we obtain sufficient conditions for the uniform stability of the zero solution of the delay differential equation with impulses

     

Asymptotic properties of solutions to linear non-autonomous neutral differential equations

In this article we study asymptotic properties of solutions to first order linear neutral differential equations with variable coefficients and constant delays. Results are stated in terms of the solution to a characteristic equation. By doing this, we extend some of the results obtained for delay equations in [J.G. Dix, Ch.G. Philos, I.K. Purnaras, An asymptotic property of solutions to linear non-autonomous delay differential equations, Electron. J. Differential Equations 2005 (2005) 1-9] to neutral equations.