A nonlinear system of differential equations with distributed delays

Chocholatý, Pavol

Displaying similar documents to “A nonlinear system of differential equations with distributed delays”

Boundedness of Third-order Delay Differential Equations in which $h$ is not necessarily Differentiable

Mathew O. Omeike (2015)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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In this paper we study the boundedness of solutions of some third-order delay differential equation in which $h (x)$ is not necessarily differentiable but satisfy a Routh–Hurwitz condition in a closed interval $[δ, k a b] \subset (0, a b)$ .

Delay-dependent stability conditions for fundamental characteristic functions

Hideaki Matsunaga (2023)

Archivum Mathematicum

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This paper is devoted to the investigation on the stability for two characteristic functions $f_{1} (z) = z^{2} + p e^{- z τ} + q$ and $f_{2} (z) = z^{2} + p z e^{- z τ} + q$ , where $p$ and $q$ are real numbers and $τ > 0$ . The obtained theorems describe the explicit stability dependence on the changing delay $τ$ . Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.

Oscillation theorems for third order nonlinear delay difference equations

Kumar S. Vidhyaa, Chinnappa Dharuman, Ethiraju Thandapani, Sandra Pinelas (2019)

Mathematica Bohemica

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Sufficient conditions are obtained for the third order nonlinear delay difference equation of the form $Δ (a_{n} (Δ (b_{n} {(Δ y_{n})}^{α}))) + q_{n} f (y_{σ (n)}) = 0$ to have property $(A)$ or to be oscillatory. These conditions improve and complement many known results reported in the literature. Examples are provided to illustrate the importance of the main results.

Necessary and sufficient conditions for oscillations of delay partial difference equations

Bing Gen Zhang, Shu Tang Liu (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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This paper is concerned with the delay partial difference equation (1) $A_{m + 1, n} + A_{m, n + 1} - A_{m, n} + Σ_{i = 1}^{u} p_{i} A_{m - k_{i}, n - l_{i}} = 0$ where $p_{i}$ are real numbers, $k_{i}$ and $l_{i}$ are nonnegative integers, u is a positive integer. Sufficient and necessary conditions for all solutions of (1) to be oscillatory are obtained.

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

Robust observer-based finite-time $H_{\infty}$ control designs for discrete nonlinear systems with time-varying delay

Yali Dong, Huimin Wang, Mengxiao Deng (2021)

Kybernetika

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This paper investigates the problem of observer-based finite-time $H_{\infty}$ control for the uncertain discrete-time systems with nonlinear perturbations and time-varying delay. The Luenberger observer is designed to measure the system state. The observer-based controller is constructed. By constructing an appropriated Lyapunov-.Krasovskii functional, sufficient conditions are derived to ensure the resulting closed-loop system is $H_{\infty}$ finite-time bounded via observer-based control. The observer-based...

On the positive bounded Solutions of linear delay higher order differential equations

Lu-San Chen, Cheh-Chih Yeh (1976)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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Si dànno condizioni sufficienti perché l’equazione $L_{n}x(t)+(-1)^{n+1}a(t)x(g(t))=0$ abbia soluzione positiva limitata.

Positive periodic solutions of a neutral functional differential equation with multiple delays

Yongxiang Li, Ailan Liu (2018)

Mathematica Bohemica

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This paper deals with the existence of positive $ω$ -periodic solutions for the neutral functional differential equation with multiple delays ${(u (t) - c u (t - δ))}^{'} + a (t) u (t) = f (t, u (t - τ_{1}), \dots, u (t - τ_{n})) .$ The essential inequality conditions on the existence of positive periodic solutions are obtained. These inequality conditions concern with the relations of $c$ and the coefficient function $a (t)$ , and the nonlinearity $f (t, x_{1}, \dots, x_{n})$ . Our discussion is based on the perturbation method of positive operator and fixed point index theory in cones.

Functional equations of delay type in $L^{1}$ spaces

Rosanna Villella-Bressan (1985)

Annales Polonici Mathematici

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Solutions of an advance-delay differential equation and their asymptotic behaviour

Gabriela Vážanová (2023)

Archivum Mathematicum

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The paper considers a scalar differential equation of an advance-delay type $\dot{y} (t) = - (a_{0} + \frac{a_{1}}{t}) y (t - τ) + (b_{0} + \frac{b_{1}}{t}) y (t + σ),$ where constants $a_{0}$ , $b_{0}$ , $τ$ and $σ$ are positive, and $a_{1}$ and $b_{1}$ are arbitrary. The behavior of its solutions for $t \to \infty$ is analyzed provided that the transcendental equation $λ = - a_{0} e^{- λ τ} + b_{0} e^{λ σ}$ has a positive real root. An exponential-type function approximating the solution is searched for to be used in proving the existence of a semi-global solution. Moreover, the lower and upper estimates are given for such a solution.

Stable periodic solutions in scalar periodic differential delay equations

Anatoli Ivanov, Sergiy Shelyag (2023)

Archivum Mathematicum

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A class of nonlinear simple form differential delay equations with a $T$ -periodic coefficient and a constant delay $τ > 0$ is considered. It is shown that for an arbitrary value of the period $T > 4 τ - d_{0}$ , for some $d_{0} > 0$ , there is an equation in the class such that it possesses an asymptotically stable $T$ -period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The...

Oscillation criteria for two dimensional linear neutral delay difference systems

Arun Kumar Tripathy (2023)

Mathematica Bohemica

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In this work, necessary and sufficient conditions for the oscillation of solutions of 2-dimensional linear neutral delay difference systems of the form $Δ [\begin{matrix} x (n) + p (n) x (n - m) \\ y (n) + p (n) y (n - m) \end{matrix}] = [\begin{matrix} a (n) & b (n) \\ c (n) & d (n) \end{matrix}] [\begin{matrix} x (n - α) \\ y (n - β) \end{matrix}]$ are established, where $m > 0$ , $α \geq 0$ , $β \geq 0$ are integers and $a (n)$ , $b (n)$ , $c (n)$ , $d (n)$ , $p (n)$ are sequences of real numbers.