An Extension of Kato’s Stability Condition for Nonautonomous Cauchy Problems
نویسندگان
چکیده
An extension of Kato’s stability condition for nonautonomous Cauchy problems is presented. It is proved that in the commutative case this condition and a mild regularity assumption imply wellposedness. If one supposes the Kato-stability, then the solutions are given by an integral formula. By means of examples we show that in general these stability conditions cannot be omitted in our results. Moreover, it is seen that the Kato-stability is not necessary for wellposedness. 1991 Mathematics Subject Classification:
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