Perturbation theorems for local integrated semigroups
We apply the contraction mapping theorem to establish some bounded and unbounded perturbation theorems concerning nondegenerate local $\alpha $-times integrated semigroups. Some unbounded perturbation results of Wang et al. [Studia Math. 170 (2005)] are also generalized. We also establish some growth properties of perturbations of local $\alpha $-times integrated semigroups.