Exponential formula for one-time integrated semigroups.
We consider the equation , where is the generator of an analytic semigroup on a Banach space , is a variable bounded operator in . It is assumed...
Using extrapolation spaces introduced by Da Prato-Grisvard and Nagel we prove a non-autonomous perturbation theorem for Hille-Yosida operators. The abstract result is applied to non-autonomous retarded partial differential equations.