This is the abstract of the paper
  "Sufficiency of Lipschitz Conditions for Strict Solutions of Linear Evolution Equations in Nonreflexive Spaces"
by Stefano Bertoni.

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  get evolve-l 01-00053

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"http://maserv.mathematik.uni-karlsruhe.de/~mi1weis/evolve-l/index.html"

too.

Abstract:
In this paper we give sufficient conditions of existence for strict
solutions of the nonautonomous linear problem $u'(t)=A(t)\,u(t)$ in a
Banach space, in the case $D(A(t))=D=$ constant.
With respect to the classic Kato's sufficient conditions we need only
$t\mapsto A(t)$ continuous and of bounded variation in ${\cal L}(D,X)$,
also if $X$ is not reflexive.
The same result can be extended to the case of nonconstant domain, with
a common subspace $Y\subseteq D(A(t))$.

The main tool is the Stieltjes integral of operators in Banach spaces.

Keywords: evolutionary processes, CD-systems, functions of bounded
variation, strict solutions, Stieltjes integral, Volterra-Stieltjes
equations.

AMS subject classification: 34G10 (47D06).