Periodic solutions of second-order differential equations in Hilbert spaces
type: Item
instance of: scholarly article
title: Periodic solutions of second-order differential equations in Hilbert spaces
zbMATH Open document ID: 1482.34110
author: Giuliano Klun
author: Andrea Sfecci
author: Alessandro Fonda
published in: Mediterranean Journal of Mathematics
publication date: 2021-09-20T00:00:00Z
review text: Classical existence results for the scalar periodic problem \[\begin{cases} \ddot x=f(t,x), \\ x(0)=x(T),\;\; \dot x(0)=\dot x(T), \end{cases} \] where \(f:[0,T]\times \mathbb{R}\to \mathbb{R}\) is continuous, are extended to systems, both in a finite-dimensional setting (\(f:[0,T]\times \mathbb{R}^N\to \mathbb{R}^N\)) and in an infinite- dimensional setting (\(f:[0,T]\times H\to H\), \(H\) is a separable Hilber space). The method of lower/upper solutions is used in both the well-ordered and non-well-ordered cases.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7397621
zbMATH Keywords: periodic solutions
zbMATH Keywords: lower and upper solutions
zbMATH Keywords: degree theory
zbMATH Keywords: infinite-dimensional dynamical systems
Wikidata QID: Q115390246
MaRDI profile type: Publication
full work available at URL: s00009-021-01857-8
OpenAlex ID: W3197475765
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DOI: 10.1007/S00009-021-01857-8
description: scientific article; zbMATH DE number 7397621