This paper deals with the exponential stability of a class of nonlinear delay-integrodifferential equations of the form ẋ(t) = f ( t, x(t), x(t − τ1(t)), ∫ t t−τ2(t) g(t, s, x(s))ds ) , t ≥ t0, where τi(t) > 0 for i = 1, 2 and t ≥ t0. The stability relation between ordinary and delay-integro-differential equations is given. It is shown under some suitable conditions that a delay-integro-differe...

Some new stability results are given for a delay integro-differential equation. A basis theorem on the behavior of solutions of delay integro-differential equations is established. As a consequence of this theorem, a stability criterion is obtained.

We study travelling kinks in the spatial discretizations of the nonlinear Klein–Gordon equation, which include the discrete φ lattice and the discrete sine–Gordon lattice. The differential advance-delay equation for travelling kinks is reduced to the normal form, a scalar fourth-order differential equation, near the quadruple zero eigenvalue. We show numerically non-existence of monotonic kinks...

Delay differential equations are a class of mathematical models describing various natural and engineered phenomena with delayed feedbacks in the system. Mathematical theory of delay differential equations or functional-differential equations have been developed in the second half of twentieth century to study mathematical questions from models of population biology, biochemical reactions, neur...

In this paper, a definition of the fundamental operator for the linear autonomous functional differential equation with infinite delay in a Banach space is given, and some sufficient and necessary conditions of the fundamental operator being exponentially stable in abstract phase spaces which satisfy some suitable hypotheses are obtained. Moreover, we discuss the relation between the exponentia...

In this paper, we give sufficient conditions to guarantee exponential decay of solutions to zero of the time varying delay differential equation of first order. By using the Lyapunov-Krasovskii functional approach, we establish new results on the exponential decay of solutions, which include and improve some related results in the literature. of linear impulsive differential equations with dist...

algebraic-delay differential systems and age structured population dynamics Jianhong Wu York University, Canada [email protected] N. Kosovalic, F.M.G. Magpantay, Y. Chen We present some recent results on the fundamental theory and numerical analysis of algebraic-delay differential systems, and discuss its motivation from and applications to structured population dynamics. On the basins of attractio...

In this paper, the following third-order nonlinear delay differential equation with periodic coefficients x′′′(t) + p(t)x′′(t) + q(t)x′(t) + r(t)x(t) = f (t, x (t) , x(t− τ(t))) + d dt g (t, x (t− τ (t))) , is considered. By employing Green’s function, Krasnoselskii’s fixed point theorem and the contraction mapping principle, we state and prove the existence and uniqueness of periodic solutions...

The second order nonlinear delay differential equation with periodic coefficients x ′′(t)+ p(t)x ′(t)+ q(t)x(t) = r(t)x ′(t − τ(t))+ f (t, x(t), x(t − τ(t))), t ∈ R is considered in this work. By using Krasnoselskii’s fixed point theorem and the contraction mapping principle, we establish some criteria for the existence and uniqueness of periodic solutions to the delay differential equation. c ...

In this paper, some new types of delay integral inequalities on time scales are established, which can be used as a handy tool in the investigation of making estimates for bounds of solutions of delay dynamic equations on time scales. Our results generalize the main results in [15, 16, 17], and some of the results in [18, 19]. Key–Words: Delay integral inequality; Time scale; Integral equation;...