Sufficient Conditions for Exponential Stability and Dichotomy of Evolution Equations
نویسنده
چکیده
We present several suucient conditions for exponential stability and di-chotomy of solutions of the evolution equation u 0 (t) = A(t)u(t) () on a Banach space X. Our main theorem says that if the operators A(t) generate analytic semigroups on X having exponential dichotomy with uniform constants and A() has a suuciently small HH older constant, then () has exponential dichotomy. We further study robustness of exponential dichotomy under time dependent unbounded Miyadera-type perturbations. Our main tool is a characterization of exponential dichotomy of evolution families by means of the spectra of the so-called evolution semigroup on C 0 (R; X) or L 1 (R; X).
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