Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 23, No 1, (1997), 69p-94p
We study, in Carathéodory assumptions, existence, continuation
and continuous dependence of extremal solutions for an abstract and rather
general class of hereditary differential equations. By some examples we prove
that, unlike the nonfunctional case, solved Cauchy problems for hereditary
differential equations may not have local extremal solutions.