Almost exponential stability and exponential stability of resolvent operator families

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• 作者：Zhenbin Fan ; Qixiang Dong ; Gang Li
• 关键词：Exponential stability ; Volterra equation ; Resolvent family ; Abstract integral equations
• 刊名：Semigroup Forum
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：93
• 期：3
• 页码：491-500
• 全文大小：387 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Algebra
  
• 出版者：Springer New York
• ISSN：1432-2137
• 卷排序：93

文摘

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.