ABSTRACT
The Cauchy problems for differential equations in abstract spaces have been extensively developed in various directions in recent years. From a great deal of papers on this subject, we notice that the situation when the abstract space is a locally convex space has been discussed (e.g. Fattorini (1968,1969), Henriquez-Hernández (1992), Konishi (1971), Miyadera (1959), Xiao-Liang (1992a)) to satisfy the need of solving the various problems arising from applied fields.
