This article deals with some solvability results on the Cauchy problem for linear differential equations with unbounded operators. The main result consists in the description of the set of initial data for which the corresponding solutions are represented by means of the classical exponential formula in the stationary case, and by means of the Peano matriciant formula in the non-stationary case. In this connection a new generalization of Gelfand’s lemma about analytic vectors of the generator of a strongly continuous group is proved.
Cite this article
E.A. Barkova, P. P. Zabrejko, On the Solvability of Linear Differential Equations with Unbounded Operators in Banach Spaces. Z. Anal. Anwend. 17 (1998), no. 2, pp. 339–360DOI 10.4171/ZAA/826