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Zbl 0995.34038
Nguyen Van Minh; Nguyen Thieu Huy
Characterizations of dichotomies of evolution equations on the half-line. (English)
[J] J. Math. Anal. Appl. 261, No.1, 28-44 (2001). ISSN 0022-247X

The authors characterize (ordinary and exponential) dichotomies of an evolution family $U(t,s)$, $t \geq s$, of bounded linear operators on a Banach space $X$ in terms of properties of certain operators $I_0$ and $I_X$ which are defined on subspaces of $L_p(\bbfR_+,X)$ using the integral equation $$ u(t) = U(t,s) u(s) + \int_s^t U(t,\xi) f(\xi) d\xi .$$
[Stefan Siegmund (Augsburg)]

MSC 2000:: *34D09 Dichotomy, trichotomy
34G10 Linear ODE in abstract spaces
47D03 (Semi)groups of linear operators

Keywords: exponential dichotomy; ordinary dichotomy; evolution equation

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