International Journal of Partial Differential Equations http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Integrally Small Perturbations of Semigroups and Stability of Partial Differential Equations Sun, 28 Apr 2013 14:09:34 +0000 http://www.hindawi.com/journals/ijpde/2013/207581/ 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. Michael Gil' Copyright © 2013 Michael Gil'. All rights reserved.