Characterizations of dichotomies of evolution equations on the half-line

Authors
Van Minh, N Huy, NT
Citation
N. Van Minh et Nt. Huy, Characterizations of dichotomies of evolution equations on the half-line, J MATH ANAL, 261(1), 2001, pp. 28-44
Citations number
15
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
ISSN journal
0022247X → ACNP
Volume
261
Issue
1
Year of publication
2001
Pages
28 - 44
Database
ISI
SICI code
0022-247X(20010901)261:1<28:CODOEE>2.0.ZU;2-U
Abstract
In this paper we investigate the characterization of dichotomies of an evol ution family U = (U(t, s))(t greater than or equal tos greater than or equa l to0) of bounded linear operators on Banach space X. We introduce operator s I-0 and I-X on subspaces of L-p(R+, X) using the integral equation u(t) = U(t, s)u(s) + integral'(s) U(t, xi )f (xi )d xi. The exponential and ordin ary dichotomies of U are characterized by properties of I-0, I-X. (C) 2001 Academic Press.