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A general nonautonomous Nicholson equation with multiple pairs of delays in {\it mixed monotone} nonlinear terms is studied. Sufficient conditions for permanence are given, with explicit lower and upper uniform bounds for all positive…

Classical Analysis and ODEs · Mathematics 2023-09-06 Teresa Faria

We consider initial-boundary-value problems for a class of nonlinear third order equations having non-autonomous forcing terms and get new asymptotic stability results by means of the Liapunov second method. The class includes equations…

Mathematical Physics · Physics 2012-09-28 Armando D'Anna , Gaetano Fiore

In this paper, we study the $L^p$-asymptotic stability with $p\in (1,\infty)$ of the one-dimensional nonlinear damped wave equation with a localized damping and Dirichlet boundary conditions in a bounded domain $(0,1)$. We start by…

Analysis of PDEs · Mathematics 2022-08-05 Meryem Kafnemer , Yacine Chitour

This paper investigates the local asymptotic stabilization of a very general class of instable autonomous nonlinear difference equations which are subject to perturbed dynamics which can have a different order that that of the nominal…

Dynamical Systems · Mathematics 2011-08-02 M. De La Sen

In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…

Optimization and Control · Mathematics 2026-04-30 Picchiotti Flavio , Thiago Alves Lima , Girard Antoine

An equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally asymptotically stable for all delays. We present criteria for absolute stability of DDEs with discrete time-delays. In the case of a single delay,…

Dynamical Systems · Mathematics 2021-03-23 Serhiy Yanchuk , Matthias Wolfrum , Tiago Pereira , Dmitry Turaev

We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for…

Analysis of PDEs · Mathematics 2007-05-23 M. I. Caiado , A. V. Sarychev

Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…

Dynamical Systems · Mathematics 2024-05-10 Anatoli Ivanov , Sergiy Shelyag

We study the steady states and dynamics of a thin film-type equation with non-conserved mass in one dimension. The evolution equation is a nonlinear fourth-order degenerate parabolic PDE motivated by a model of volatile viscous fluid films…

Analysis of PDEs · Mathematics 2019-10-29 Hangjie Ji , Thomas P. Witelski

This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…

Analysis of PDEs · Mathematics 2022-08-31 Nicolas Vanspranghe , Francesco Ferrante , Christophe Prieur

This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…

Dynamical Systems · Mathematics 2017-08-18 Bin Zhou

This paper deals with the asymptotic behavior of solutions to the delayed monostable equation: $(*)$ $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) + g(u(t-h,x)),$ $x \in \mathbb{R},\ t >0,$ where $h>0$ and the reaction term $g: \mathbb{R}_+ \to…

Analysis of PDEs · Mathematics 2017-04-12 Abraham Solar

We introduce a delay nonlinear differential equation model which describes how fish are harvested. In our previous studies we investigated the persistence of that equation and existence of a periodic solution for this equation. Here we…

Dynamical Systems · Mathematics 2007-05-23 L. Berezansky , L. Idels

This article studies a class of semilinear scalar field equations on the real line with variable coefficients in the linear terms. These coefficients are not necessarily small perturbations of a constant. We prove that under suitable…

Analysis of PDEs · Mathematics 2023-08-15 Mashael Alammari , Stanley Snelson

Adapting a counterexample recently proposed by J.L. Mancilla-Aguilar and H. Haimovich, we show here that, for time-delay systems, global asymptotic stability does not ensure that solutions converge uniformly to zero over bounded sets of…

Systems and Control · Electrical Eng. & Systems 2024-03-04 Antoine Chaillet , Fabian Wirth , Andrii Mironchenko , Lucas Brivadis

For the nonlinear Dirac equation in (1+1)D with scalar self-interaction (Gross--Neveu model), with quintic and higher order nonlinearities (and within certain range of the parameters), we prove that solitary wave solutions are…

Analysis of PDEs · Mathematics 2014-07-07 Andrew Comech , Tuoc Van Phan , Atanas Stefanov

In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical…

Dynamical Systems · Mathematics 2013-02-11 Yajing Li , Yejuan Wang

In this paper, we are concerned with the compressible Euler-Maxwell equations with a nonconstant background density (e.g. of ions) in three dimensional space. There exist stationary solutions when the background density is a small…

Analysis of PDEs · Mathematics 2014-03-27 Qingqing Liu , Changjiang Zhu

In this work we study the asymptotic behavior of solutions for a general linear second-order evolution differential equation in time with fractional Laplace operators in $\mathbb{R}^n$. We obtain improved decay estimates with less demand on…

Analysis of PDEs · Mathematics 2018-02-06 M. F. G. Palma , C. R. da Luz

We present a stability result for a wide class doubly nonlinear equations, featuring general maximal monotone operators, and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis resides on the reformulation of the…

Analysis of PDEs · Mathematics 2013-02-19 Thomas Roche , Riccarda Rossi , Ulisse Stefanelli