Necessary and sufficient conditions for the oscillations of a multiplicative delay logistic equation

Necessary and sufficient conditions for oscillations of first order neutral delay difference equations with constant coefficients

In this paper, we establish the necessary and sufficient conditions for oscillation of the following first order neutral delay difference equation ∆[x(n) + px(n− τ)] + qx(n− σ) = 0, n ≥ n0, (∗) where τ and σ are positive integers, p 6= 0 is a real number and q is a positive real number. We proved that every solution of (∗) oscillates if and only if its characteristic equation (λ− 1)(1 + pλ−τ ) ...

Necessary and Sufficient Conditions for Oscillations of Neutral Delay Difference Equations with Several Coefficients

Global Attractivity and Oscillations in a Periodic Delay - Logistic Equation

in which r and K are positive numbers; r is related to the reproduction of the species while K is related to the capacity of the environment to sustain the population. It is assumed that there is no immigration or emigration and other characteristics such as age dependence and interactions with other species are assumed to be not significant. Elementary analysis of (1.1) indicates that the solu...

Necessary and Sufficient Conditions for Delay-Dependent Asymptotic Stability of Linear Discrete Time Delay Autonomous Systems

This paper offers new, necessary and sufficient conditions for delay-dependent asymptotic stability of systems of the form 0 1 ( 1) ( ) ( ) x k A x k A x k h + = + − . The time-dependent criteria are derived by Lyapunov’s direct method. Two matrix equations have been derived: matrix polynomial equation and discrete Lyapunov matrix equation. Also, modifications of the existing sufficient conditi...

The necessary and sufficient conditions of Hyers-Ulam stability for a class of parabolic equation

The aim of this paper is to consider the Hyers-Ulam stability of a class of parabolic equation { ∂u ∂t − a 2∆u+ b · ∇u+ cu = 0, (x, t) ∈ Rn × (0,+∞), u(x, 0) = φ(x), x ∈ Rn. We conclude that (i) it is Hyers-Ulam stable on any finite interval; (ii) if c 6= 0, it is Hyers-Ulam stable on the semi-infinite interval; (iii) if c = 0, it is not Hyers-Ulam stable on the semi-infinite interval by using ...