Periodic solutions for second order differential inclusions with nonconvex and unbounded multifunction
type: Item
instance of: scholarly article
title: Periodic solutions for second order differential inclusions with nonconvex and unbounded multifunction
zbMATH Open document ID: 0939.34013
DOI: 10.1023/A:1006644519896
author: Evgenios P. Avgerinos
author: Nikolaos S. Papageorgiou
author: Nikos Yannakakis
published in: Acta Mathematica Hungarica
publication date: 2000-02-21T00:00:00Z
review text: The authors consider boundary value problems \(x''(t) \in F\big(t,x(t),x'(t)\big)\) a.e. on \([0,b],\) \(x(0)=x(b)\) and \(x'(0)=x'(b),\) where \(F\) is an unbounded and nonconvex set-valued function. They transform it into a periodic problem with convex and bounded right-hand side via Filippov regularization of a directionally continuous selector and show that solutions to the latter problem also solve the original problem. The paper generalizes results of \textit{S. Hu} and \textit{N. S. Papageorgiou} [Proc. Am. Math. Soc. 123, No.~10, 3043-3050 (1995; Zbl 0851.34014)] where the authors studied first-order periodic differential inclusions with a nonconvex multifunction by a similar approach.
reviewed by: David S. Boukal
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 49K24
zbMATH DE Number: 1404412
zbMATH Keywords: differential inclusions
zbMATH Keywords: boundary value problems
MaRDI profile type: Publication
full work available at URL: a:1006644519896
OpenAlex ID: W2018746152
description: scientific article; zbMATH DE number 1404412