Almost exponential stability and exponential stability of resolvent operator families

• DOI: 10.1007/s00233-016-9811-z
• Publication Date: 2016-07-01T14:53:41Z
• Authors: Zhenbin Fan; Qixiang Dong; Gang Li
• Keywords: Operator (biology); Resolvent formalism; Exponential formula

In this paper, we introduce a new concept of stability of resolvent operator families, almost exponential stability. We establish a perturbation theorem on analytic resolvent operator families, and derive some sufficient conditions on the almost exponential stability or exponential stability of resolvent operator families by using rescaling technique and contour integral approach. Our theorems generalize corresponding results for semigroups.