Characterizations of dichotomies of evolution equations on the half-line

Journal of Mathematical Analysis and Applications

Volumn 261, Issue 1, 2001, Pages 28-44

  Van Minh, Nguyen ^a   Huy, Nguyen Thieu ^b  

^a UNIVERSITY OF ELECTRO COMMUNICATIONS   (Japan)

^b HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Viet Nam)

Author keywords

Evolution equations; Evolution family; Exponential dichotomy; Integral equation; Ordinary dichotomy

Indexed keywords

EID: 0035457177     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2001.7450     Document Type: Article

References (15)

1. Aulbach B., Minh N. V. Semigroups and exponential stability of nonautonomous linear differential on the half-line. Agrawal R. P. Dynamical Systems and Application. 1995;45-61 World Scientific, Singapore.
2. Daleckii Ju. L., Krein M. G. Stability of solution of differential equation in Banach spaces. Trans. Amer. Math. Soc. 1974.
3. Datko R. Uniform asymptotic stability of evolutionary processes in a Banach space. SIAM J. Math. Anal. 3:1972;428-445.
4. Levitan B. M., Zhikov V. V. Almost Periodic Functions and Differential Equations. 1978;Moscow Univ. Publ. House.
5. Y. Latushkin, S. Montgomery Smith, and T. Randolph, Evolutionary semigroups and robust stability of evolution operators on Banach spaces, preprint.
6. Massera J. J., Schäffer J. J. Linear Differential Equations and Function Spaces. 1966;Academic Press, New York.
7. Minh N. V. On the proof of characterization of the exponential dichotomy. Proc. Amer. Math. Soc. 127:1999;779-782.
8. Minh N. V., Rabiger F., Schnaubelt R. Exponential dichotomy exponential expansiveness and exponential dichotomy of evolution equation on the half line. Integral Equations Operator Theory. 32:1998;332-353.
9. Murakami S., Naito T., Minh N. V. Evolution semigroups and sums of commuting operators: A new approach to the admissibility of function spaces. J. Differential Equations. 164:2000;240-285.
10. Nagel R. One-Parameter Semigroups of Positive Operators. Lecture Notes in Math. 1184:1986;Springer-Verlag, Berlin/Heidelberg.
11. Naito T., Minh N. V. Evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations. J. Differential Equations. 152:1999;358-376.
12. van Neerven J. The Asymptotic Behaviour of Semigroups of Linear Operator. Operator Theory, Advances and Applications. 88:1996;Birkhäuser, Basel.
13. Pazy A. Semigroup of Linear Operators and Application to Partial Differential Equations. 1983;Springer-Verlag, Berlin.
14. Perron O. Die Stabilitätsfrage bei Differentialgleichungen. Math. Z. 32:1930;703-728.
15. Zhang W. The Fredhom alternative and exponential dichotomies for parabolic equations. J. Math. Anal. Appl. 191:1995;180-201.