Convergence to equilibria in a differential equation with small delay

Mihály Pituk

Displaying similar documents to “Convergence to equilibria in a differential equation with small delay”

Convergence to equilibria in a differential equation with small delay

Pituk, Mihály

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An analysis on the stability of a state dependent delay differential equation

Sertaç Erman, Ali Demir (2016)

Open Mathematics

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In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t). $τ (u (t)) = \frac{a + b u (t)}{c + b u (t)} .$ Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.

On the existence of positive solutions of second order neutral difference equations

Wen-Xian Lin (2004)

Applicationes Mathematicae

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The neutral delay difference equations of second order with positive and negative coefficients $Δ ² (x ₙ + p ₙ x_{n - τ}) + q ₙ x_{n - σ} - r ₙ x_{n - λ} = 0$ , n = 0,1,2,... studied sufficient condition existence positive solution equation obtained

Behaviour of solutions of linear differential equations with delay

Josef Diblík (1998)

Archivum Mathematicum

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This contribution is devoted to the problem of asymptotic behaviour of solutions of scalar linear differential equation with variable bounded delay of the form $\dot{x} (t) = - c (t) x (t - τ (t)) (^{*})$ with positive function $c (t) .$ Results concerning the structure of its solutions are obtained with the aid of properties of solutions of auxiliary homogeneous equation $\dot{y} (t) = β (t) [y (t) - y (t - τ (t))]$ where the function $β (t)$ is positive. A result concerning the behaviour of solutions of Eq. (*) in critical case is given and, moreover, an analogy with behaviour of...