CÁC BÀI BÁO KHOA HỌC 18:13:47 Ngày 21/11/2019 GMT+7
Exponential stability, exponential expansiveness, and exponential dichotomy of evolution equations on the half-line

Let U = (U(t, s))t≥s≥0 be an evolution family on the half-line of bounded linear operators on a Banach space X. We introduce operators G0, GX and IX on certain spaces of X-valued continuous functions connected with the integral equation u(t) = U(t, s)u(s) + ∫ts U(t, ξ)f/(ξ)dξ, and we characterize exponential stability, exponential expansiveness and exponential dichotomy of U by properties of G0, GX and IX, respectively. This extends related results known for finite dimensional spaces and for evolution families on the whole line, respectively.

 Van Minh N., Rabiger F., Schnaubelt R.
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