Exponential dichotomies of linear dynamic equations on measure chains under slowly varying coefficients

Journal of Mathematical Analysis and Applications

Volumn 289, Issue 1, 2004, Pages 317-335

  Pötzsche, Christian ^a  

^a UNIVERSITY OF AUGSBURG   (Germany)

Author keywords

Exponential dichotomy; Linear dynamic equation; Slowly varying; Time scale

Indexed keywords

EID: 0347577812     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2003.09.063     Document Type: Article

References (18)

1. B. Aulbach, S. Hilger, Linear dynamic processes with inhomogeneous time scale, in: G.A. Leonov, et al. (Eds.), Nonlinear Dynamics and Quantum Dynamical Systems, Akademie-Verlag, Berlin, 1990, pp. 9-20.
2. M. Bohner, A. Peterson, Dynamic Equations on Time Scales - An Introduction with Applications, Birkhäuser, Boston, 2001.
3. W.A. Coppel, Dichotomies in Stability Theory, in: Lecture Notes in Mathematics, Vol. 629, Springer-Verlag, Berlin, 1978.
4. C.V. Coffman, J.J. Schäffer, Dichotomies for linear difference equations, Math. Ann. 172 (1967) 139-166.
5. J.L. Daleckiǐ, M.G. Kreǐn, Stability of Solutions of Differential Equations in Banach Space, in: Translations of Mathematical Monographs, Vol. 43, American Mathematical Society, Providence, RI, 1974.
6. D. Henry, Geometric Theory of Semilinear Parabolic Equations, in: Lecture Notes in Mathematics, Vol. 840, Springer-Verlag, Berlin, 1980.
7. S. Hilger, Analysis on measure chains - a unified approach to continuous and discrete calculus, Results Math. 18 (1990) 18-56.
8. R.A. Johnson, Remarks on linear differential systems with measurable coefficients, Proc. Amer. Math. Soc. 100 (1987) 491-504.
9. J. Kalkbrenner, Exponential Dichotomy and Chaotic Dynamic of Noninvertible Difference Equations, Ph.D. thesis, University of Augsburg, 1994, in German.
10. J.S. Muldowney, Dichotomies and asymptotic behaviour for linear differential systems, Trans. Amer. Math. Soc. 283 (1984) 465-484.
11. K.J. Palmer, A perturbation theorem for exponential dichotomies, Proc. Roy. Soc. Edinburgh Sect. A 106 (1987) 25-37.
12. C. Pötzsche, Exponential dichotomies for linear dynamic equations, Nonlinear Anal. 47 (2001) 873-884.
13. C. Pötzsche, Slow Fiber Bundles of Dynamic Equations on Measure Chains, Ph.D. thesis, University of Augsburg, 2002, in German.
14. C. Pötzsche, Slow and fast variables in nonautonomous difference equations, J. Difference Equations Appl. 9 (2003) 473-487.
15. K. Sakamoto, A remark on perturbation theorems for exponential dichotomies, private correspondence, March 2000.
16. K. Sakamoto, Estimates on the strength of exponential dichotomies and application to integral manifolds, J. Differential Equations 107 (1994) 259-279.
17. R.J. Sacker, G.R. Sell, A spectral theory for linear differential systems, J. Differential Equations 27 (1978) 320-358.
18. N. Van Minh, Spectral theory for linear non-autonomous differential equations, J. Math. Anal. Appl. 187 (1994) 339-351.