Zeitschrift für Analysis und ihre Anwendungen
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Published online: 1998-06-30
On the Solvability of Linear Differential Equations with Unbounded Operators in Banach SpacesE.A. Barkova and P. P. Zabrejko (1) Belgos University, Minsk, Belarus
(2) The Academy of Sciences of Belarus, Minsk, Belarus
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.
Keywords: Banach spaces, linear differential equations with unbounded operators, abstract Cauchy problems, Roumieu spaces, Gevrey spaces, Beurling spaces
Barkova E.A., Zabrejko P. P.: On the Solvability of Linear Differential Equations with Unbounded Operators in Banach Spaces. Z. Anal. Anwend. 17 (1998), 339-360. doi: 10.4171/ZAA/826