Abstract
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.
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Acknowledgments
The work was supported by the NSF of China (11571300,11271316), the Qing Lan Project of Jiangsu Province of China and High-Level Personnel Support Program of Yangzhou University.
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Communicated by Abdelaziz Rhandi.
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Fan, Z., Dong, Q. & Li, G. Almost exponential stability and exponential stability of resolvent operator families. Semigroup Forum 93, 491–500 (2016). https://doi.org/10.1007/s00233-016-9811-z
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DOI: https://doi.org/10.1007/s00233-016-9811-z