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Hölder’s characterizations for the uniform exponential stability of linear skew-product semiflows in Banach spaces. (Chinese. English summary) Zbl 1463.34252

Summary: The aim of this paper is to give several Hölder’s characterizations for uniform exponential stability properties of linear skew-product semiflows in Banach space \(X\) and its dual space \(X^*\). The necessary and sufficient conditions for uniform exponential stability are obtained via functional analysis and operator theory. The results extend some well-known conclusions in stability theory.

MSC:

34G10 Linear differential equations in abstract spaces
34D20 Stability of solutions to ordinary differential equations
47D03 Groups and semigroups of linear operators
47D06 One-parameter semigroups and linear evolution equations
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