A dynamical approach to lower and upper solutions for planar systems. ``To the memory of Massimo Tarallo''
type: Item
instance of: scholarly article
title: A dynamical approach to lower and upper solutions for planar systems. ``To the memory of Massimo Tarallo''
zbMATH Open document ID: 1478.34043
author: Alessandro Fonda
author: Rodica Toader
published in: Discrete and Continuous Dynamical Systems
publication date: 2021-06-08T00:00:00Z
review text: The theory of lower and upper solutions appears usually for some second order scalar ordinary differential equations with separated boundary conditions, which was developed in several directions, by different methods. In this paper, authors have proved the existence of bounded and periodic solutions for planar systems \[x'=f(t,x,y),\quad y'=g(t,x,y)\] by introducing a notion of lower and upper solutions, which generalizes the classical one on the existence of bounded, periodic for scalar second order equations. The new approach is based on a dynamical study of the solutions. Finally, they provide some corollaries on the existence of almost periodic solutions for scalar second order equations.
reviewed by: Qihuai Liu
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 37C60
zbMATH DE Number: 7356216
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: periodic systems
zbMATH Keywords: Ważewski method
zbMATH Keywords: Massera Theorem
zbMATH Keywords: bounded solutions
zbMATH Keywords: almost periodic solutions
MaRDI profile type: Publication
full work available at URL: dcds.2021012
OpenAlex ID: W3120174280
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DOI: 10.3934/DCDS.2021012
description: scientific article; zbMATH DE number 7356216