Let be a generator of an exponentially stable
operator semigroup in a Banach space,
and let be a linear bounded variable operator.
Assuming that is sufficiently small in a certain sense for the equation
, we derive exponential stability conditions.
Besides, we do not require that for each , the “frozen”
autonomous equation is stable. In particular, we consider
evolution equations with periodic operator coefficients.
These results are applied to partial differential equations.
Stability of integro-differential equations with periodic operator coefficients
