Phase spaces \(C_ g\), \(C_ h\), and g-uniform boundedness of FDE(ID)
type: Item
instance of: scholarly article
title: Phase spaces \(C_ g\), \(C_ h\), and g-uniform boundedness of FDE(ID)
zbMATH Open document ID: 0668.34076
DOI: 10.1016/0022-247X(89)90304-1
author: Min He
author: Ke Wang
author: Quichang Huang
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: Consider the functional differential equation with infinite delay \(\dot x=f(t,x_ t)\). In the theory of these equations, the phase space of initial functions play a very important role. \textit{J. K. Hale} and \textit{J. Kato} [Funkcial Ekvac. 21, No.1, 11-41 (1978; Zbl 0383.34055)] introduced the B phase space and \textit{T. A. Burton} (1985) the \(C_ g\) phase space. Following their clues, the authors introduced the phase space \(C_ h\) and a study of the relation between \(C_ g\) and \(C_ h\) is made. Several theorems that ensure g-uniform boundedness are given. Finally new conditions and theorems for existence of periodic solutions of Volterra equations are found.
reviewed by: C.Simirad
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 4093979
zbMATH Keywords: functional differential equation with infinite delay
zbMATH Keywords: phase space
zbMATH Keywords: g- uniform boundedness
zbMATH Keywords: Volterra equations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4093979