Massera's theorems for various types of equations with discontinuous solutions
type: Item
instance of: scholarly article
title: Massera's theorems for various types of equations with discontinuous solutions
zbMATH Open document ID: 1466.34004
author: Mateus Fleury
author: Antonín Slavík
author: Jaqueline Godoy Mesquita
published in: Journal of Differential Equations
publication date: 2020-10-13T00:00:00Z
review text: In the article under review, the authors present new Massera's type results for generalized ordinary differential equations in finite dimensional spaces \(\mathbb{R}^n\). For \(n=1\) it is proven that, under appropriate conditions, each bounded solution of the equation \[ \frac{d}{dt}x=D_t F(x,t) \] is asymptotic to a periodic solution. For the general case of a finite-dimensional space, for linear problems \[ \frac{d}{dt}x=D_t[A(t)x+f(t)] \] the existence of a solution implies the existence of a periodic solution. These results are then used to get new Massera's type theorems for measure differential equations, for dynamic equations on time scales and for impulsive differential equations with a countable number of impulses.
Mathematics Subject Classification ID: 34A06
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34A37
Mathematics Subject Classification ID: 34N05
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 7260148
zbMATH Keywords: Massera theorem
zbMATH Keywords: periodic solution
zbMATH Keywords: generalized ordinary differential equations
zbMATH Keywords: measure differential equations
zbMATH Keywords: impulsive equations
zbMATH Keywords: dynamic equations on time scales
reviewed by: Bianca Satco
MaRDI profile type: Publication
full work available at URL: j.jde.2020.08.043
OpenAlex ID: W3088875572
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DOI: 10.1016/J.JDE.2020.08.043
description: scientific article; zbMATH DE number 7260148