Uniform exponential stability of linear almost periodic systems in banach spaces

Electronic Journal of Differential Equations

Volumn 2000, Issue , 2000, Pages

  Cheban, David N ^a  

^a MOLDOVA STATE UNIVERSITY   (Moldova)

Author keywords

Almost periodic system; Asymptotically compact systems; Exponential stability; Global attractors; Non autonomous linear dynamical systems

Indexed keywords

EID: 52849101727     PISSN: 10726691     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (27)

1. B. G. Ararktsyan, The asymptotic almost periodic solutions same linear evolutionary equations, Matematicheskii sbornik.1988, v.133(175), Nol(5), p.3-10.
2. I. U. Bronshteyn, Dynamical systems, Shtiintsa, Kishinev, 1984.
3. N. Bourbaki, Varietes différentielles et analitiques. Fascicule de résultats, Hermann, Paris, 1971.
4. D. N. Cheban, Relations between the different type of stability of the linear almost periodical systems in the Banach space., Electronic Journal of Differential Equations, vol. 1999 (1999), No.46, pp.1-9. (ISSN: 1072-6691. URL: http://ejde.math.unt.edu or http://ejde.math.swt.edu (login: ftp ))..
5. D. N. Cheban, Bounded solutions of linear almost periodic differential equations, Izvestiya: Mathematics. 1998, v.62, No.3, pp.581-600.
6. D. N. Cheban, Boundedness, dissipativity and almost periodicity of the solutions of linear and quasilinear systems of differential equations, Dynamical systems and boundary value problems. Kishinev, "Shtiintsa", 1987 , pp. 143-159.
7. D. N. Cheban, Global attractors of infinite-dimensional systems,!, Bulletin of Academy of sciences of Republic of Moldova. Mathematics, 1994, No2 (15), p.12-21..
8. D. N. Cheban, Global attractors of infinite-dimensional systems,II, Bulletin of Academy of sciences of Republic of Moldova. Mathematics, 1995, Nol (17), p.28-37..
9. D. N. Cheban and D. S. Fakeeh, Global attractors of the dynamical systems without uniqueness fin RussianJ., "Sigma", Kishinev, 1994.
10. D. N. Cheban, locally dissipative dynamical systems and some their applications., Bulletin of Academy of sciences of Republic of Moldova. Mathematics, 1992, Nol (8), p.7-14..
11. D. N. Cheban, Test of the convergence of nonlinear systems by the first approximation. Differential equations and their invariants. Kishinev, "Shtiintsa", 1986, p.144-150..
12. D. N. Cheban, Global Attractors of non-autonomous Dynamical Systems and Almost Periodi Limit Regimes of Some Class of Evolutionary Equations, Anale. Fac. de Mat. §i Inform.,v.l 1999, pp.1-28.
13. D. N. Cheban, Theory of linear differential equations (selected topics), Shtiintsa, Kishinev 1980 (in Russian).
14. D. N. Cheban, The asymptotics of solutions of infinite dimensional homogeneous dynamical systems, Matematicheskie zametki [Mathematical notesJ. 1998, v.63, Nol, p.115-126 ..
15. Ph. Clement, H. J. A. M. Heijmans, S. Angenent, C.V. van Duijn and B. de Pagter, OneParameter Semigroups. CWI Monograph 5, North-Holland, Amsterdam.New York.Oxford. Tokyo, 1987.
16. C. C. Conley and R. K. Miller, Asymptotic stability without uniform stability: Almost periodic coefficients, J. Dif. Equat. 1965, v.l, pp.33-336.
17. Yu. L. Daletskii and M. G. Krein, Stability of solutions of differential equations in Banach space. Translations of Mathematical Monographs, vol.43, Amer. Math. Soc., Providence, 1974.
18. W. Hahn, The present state of Lyapunov's method, in "Nonlinear Problems" (R.E.Langer, ed.), University of Wisconsin.
19. J. Hale, Theory of functional differential equations., Mir, Moscow, 1984 (in Russian).
20. J. Hale, Asymptotic Behavior of Dissipative Systems. Mathematical surveys and Monographs, No. 25, American Mathematical Society, Providence, Rhode Island, 1988.
21. D. Henry, Geometric theory of semilinear parabolic equations publ Springer publaddr BerlinHeidelberg-New York yr 1981.
22. A. F. Izé, On a topological method for the analysis of the asymptotic behavior of dynamical systems and processes., Complex analysis, functional analysis and approximation theory, Nort-Holland 1986, pp.109-128.
23. B. M. Levitan and V. V. Zhikov, Almost periodic functions and differential equations, Cambridge Univ.Press, London, 1982.
24. J. L. Massera and J. J. Schäffer, Linear differential equations and functional analysis, I., Ann. of Math., 1958, v.67, No.2, pp. 517-573.
25. R. J. Sacker and G. R. Sell, Existence of dichotomies and invariant splittings for linear differential systems J., J. Dif. Equat. 1974, v.15, pp.429-458.
26. R. J. Sacker and G. R. Sell, Dichotomies for linear evoltionary equations in Banach spaces., J. Dif. Equat. 1994, v.113, pp.17-67.
27. B. M. Sadovsky, Condensing and asymptotic compact operators., Uspekhi Mat.Nauk., Vol. 23, No.l (163), 1972, pp.81-146.