Boundedness and periodic solutions in infinite delay systems
type: Item
instance of: scholarly article
title: Boundedness and periodic solutions in infinite delay systems
zbMATH Open document ID: 0755.34064
DOI: 10.1016/0022-247X(92)90264-E
author: Roger H. Hering
published in: Journal of Mathematical Analysis and Applications
publication date: 1992-09-27T00:00:00Z
review text: The boundedness and the existence of periodic solutions to the functional equation (1) \(x'(t)=F(t,x(t+s))\) is considered, where \(F\in {\mathcal C}(R\times C_ g,R^ n)\) and \(-h\leq s\leq 0\). Using the Lyapunov functional method conditions are established under which solutions to (1) are uniformly bounded and uniformly ultimately bounded with respect to unbounded \((C_ g)\) initial function spaces. The Lyapunov functional is also used for proving the existence of periodic solutions to (1).
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D40
zbMATH DE Number: 62785
zbMATH Keywords: boundedness
zbMATH Keywords: periodic solutions
zbMATH Keywords: functional equation
zbMATH Keywords: Lyapunov functional method
zbMATH Keywords: uniformly ultimately bounded
reviewed by: Izabela Foltyńska
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 62785