Periodic solutions for dissipative-repulsive systems
type: Item
instance of: scholarly article
title: Periodic solutions for dissipative-repulsive systems
zbMATH Open document ID: 0971.34061
author: Yong Li
author: Bo Zhang
author: Tassilo Küpper
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2001-10-30T00:00:00Z
review text: Following results are obtained in this paper: (1) If \(x'=f(t,x)\) is dissipative-repulsive, then it admits an \(\omega\)-periodic solution, where \(f: \mathbb{R}\times \mathbb{R}^n\to \mathbb{R}^n\) is continuous, locally Lipschitzian in \(x\) and \(f(t+\omega, x)=f(t,x)\) for every \(t\) and some \(\omega>0\). (2) If \(x'= F(t,x_t)\) is dissipative-repulsive, then it admits an \(\omega\)-periodic solution, where \(F:\mathbb{R}\times C\to\mathbb{R}^n\) is continuous, locally Lipschitzian in \(\varphi\in C\), \(F(t+\omega, \varphi)=F(t,\varphi)\) for all \((t,\varphi)\) and some \(\omega>0\) and \(F\) takes any bounded sets in \(C\) into bounded sets in \(\mathbb{R}^n\); here, \(C=C([-r,0], \mathbb{R}^n)\), \(r>0\). It is further shown that dissipative-repulsive systems admit equilibria. An example is given to illustrate some results.
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1558403
zbMATH Keywords: dissipative-repulsive systems
zbMATH Keywords: periodic solution
zbMATH Keywords: functional-differential equations
zbMATH Keywords: equilibria
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178207816
OpenAlex ID: W2032232357
cites work: Periodic solutions to functional differential equations
cites work: Unified boundedness, periodicity, and stability in ordinary and functional differential equations
cites work: Continuation Theorems for Periodic Perturbations of Autonomous Systems
cites work: Leray-Schauder degree for semilinear Fredholm maps and periodic boundary value problems of neutral equations
cites work: A Composite Coincidence Degree with Applications to Boundary Value Problems of Neutral Equations
cites work: Fixed point theorems and dissipative processes
cites work: Q3992992
cites work: The existence of an equilibrium for permanent systems
cites work: Periodic solutions of differential inclusions
cites work: Continuation theorems for boundary value problems
cites work: Periodic solutions and equilibrium states for functional-differential inclusions with nonconvex right-hand side
cites work: Periodic solutions of dissipative functional differential equations
cites work: Existence of periodic solutions for higher-order differential systems that are not of class D
cites work: Q5520199
DOI: 10.2748/TMJ/1178207816
description: scientific article; zbMATH DE number 1558403