Phase spaces \(C_ g\), \(C_ h\), and g-uniform boundedness of FDE(ID)
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.
functional differential equation with infinite delay
scientific article; zbMATH DE number 4093979