|
On the proof of characterizations of the exponential dichotomy
Author(s):
Nguyen
Van
Minh
Journal:
Proc. Amer. Math. Soc.
127
(1999),
779-782.
MSC (1991):
Primary 34G10, 47D06;
Secondary 47H20
MathSciNet review:
1473675
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
Abstract:
We describe explicitly the generator of the evolutionary semigroup associated with the evolutionary operator generated by the linear differential equation  . From this we give a short proof of some known characterizations of the exponential dichotomy of the above mentioned equation.
References:
- [A-M]
- Aulbach B., Nguyen Van Minh, Nonlinear semigroups and the existence and stability of solutions of semilinear nonautonomous evolution equations, Abstract and Applied Analysis 1 (1996), 351-380.
- [D-K]
- Daleckii Ju. L., Krein M.G., ``Stability of Solutions of Differential Equations in Banach Space'', Amer. Math. Soc., Providence RI, 1974. MR 50:5126
- [L-M]
- Latushkin Ju., Montgomery-Smith S., Evolutionary semigroups and Lyapunov theorems in Banach spaces J. Func. Anal. 127(1995), 173-197. MR 96k:47022
- [L-Z]
- Levitan B.M., Zhikov V.V., ``Almost Periodic Functions and Differential Equations'', Moscow Univ. Publ. House 1978. English translation by Cambridge University Press 1982. MR 84g:34004
- [M]
- Nguyen Van Minh, Semigroups and stability of nonautonomous differential equations in Banach spaces, Trans. Amer. Math. Soc., 345(1994), N.1, 223-242. MR 95a:34091
- [P]
- Pazy A., ``Semigroups of Linear Operators and Applications to Partial Differential Equations", Applied Math. Sci. 44, Springer-Verlag, Berlin-New York 1983. MR 85g:47061
- [R]
- Rau R., Hyperbolic evolutionary semigroups on vector valued function spaces, Semigroup Forum 48(1994), 107-118.
- [Zh]
- Zhikov V.V., On the theory of admissibility of pairs of function spaces, Soviet Math. Dokl. vol. 13(1972), N.4, 1108-1111.
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical
Society
with
MSC (1991):
34G10, 47D06,
47H20
Retrieve articles in all Journals with
MSC (1991):
34G10, 47D06,
47H20
Additional Information:
Nguyen
Van
Minh
Affiliation:
Department of Mathematics, The University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182, Japan
Email:
minh@matha.e-one.uec.ac.jp
DOI:
10.1090/S0002-9939-99-04640-7
PII:
S 0002-9939(99)04640-7
Keywords:
Evolutionary family,
evolutionary semigroup,
exponential dichotomy
Received by editor(s):
December 20, 1996
Received by editor(s) in revised form:
June 20, 1997
Additional Notes:
This note was written during the author's visit to the Institute of Mathematics, University of Tübingen. The support of the Alexander von Humboldt Foundation is gratefully acknowledged. He also thanks R. Nagel and the Division of Functional Analysis at the Institute for their warm hospitality and constant encouragement. Finally, he thanks the referee for the valuable suggestion to improve the presentation of this paper.
Communicated by:
Palle E. T. Jorgensen
Copyright of article:
Copyright
1999,
American Mathematical Society
|
