Perron Conditions for Uniform Exponential Expansiveness of Linear Skew-Product Flows

Monatshefte fur Mathematik

Volumn 138, Issue 2, 2003, Pages 145-157

  Megan, Mihail ^a   Sasu, Adina Luminiţa ^a   Sasu, Bogdan ^a  

^a WEST UNIVERSITY OF TIMISOARA   (Romania)

Author keywords

Linear skew product flow; Uniform exponential expansiveness

Indexed keywords

EID: 0345492034     PISSN: 00269255     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00605-002-0520-1     Document Type: Article

References (17)

1. Ben-Artzi A, Gohberg I, Kaashoek MA (1993) Invertibility and dichotomy of differential operators on the half-line. J Dynam Differ Equations 5: 1-36
2. Chicone C, Latushkin Y (1999) Evolution Semigroups in Dynamical Systems and Differential Equations. Providence, RI: Amer Math Soc
3. Chow SN, Leiva H (1995) Existence and roughness of the exponential dichotomy for linear skew-product semiflows in Banach spaces. J Differ Equations 120: 429-477
4. Chow SN, Leiva H (1996) Unbounded perturbation of the exponential dichotomy for evolution equations. J Differ Equations 129: 509-531
5. Henry D (1981) Geometric Theory of Semilinear Parabolic Equations. New York: Springer
6. Latushkin Y, Randolph T (1995) Dichotomy of differential equations on Banach spaces and an algebra of weighted translation operators. Integral Equations Operator Theory 23: 472-500
7. Latushkin Y, Montgomery-Smith S, Randolph T (1996) Evolutionary semigroups and dichotomy of linear skew-product flows on locally compact spaces with Banach fibers. J Differ Equations 125: 73-116
8. Latushkin Y, Schnaubelt R (1999) Evolution semigroups, translation algebras and exponential dichotomy of cocycles. J Differ Equations 159: 321-369
9. Megan M, Sasu AL, Sasu B (2003) Discrete admissibility and exponential dichotomy for evolution families. Discrete Contin Dynam Systems (accepted)
10. Megan M, Sasu B, Sasu AL (2002) On nonuniform exponential dichotomy of evolution operators in Banach spaces. Integral Equations Operator Theory 44: 71-78
11. Megan M, Sasu AL, Sasu B (2002) On uniform exponential stability of linear skew-product semi flows in Banach spaces. Bull Belg Math Soc Simon Stevin 9: 143-154
12. Megan M, Sasu AL, Sasu B (2002) Stabilizability and controllability of systems associated to linear skew-product semiflows. Rev Mat Complutense 15: 599-618
13. Megan M, Sasu AL, Sasu B (2001) Perron conditions and uniform exponential stability of linear skew-product semiflows on locally compact spaces. Acta Math Univ Comenian 70: 229-240
14. Van Minh N, Räbiger F, Schnaubelt R (1998) Exponential stability, exponential expansiveness and exponential dichotomy of evolution equations on the half-line. Integral Equations Operator Theory 32: 332-353
15. Perron O (1930) Die Stabilitätsfrage bei Differentialgleichungen. Math Z 32: 703-728
16. Pliss VA, Sell GR (1999) Robustness of exponential dichotomies in infinite-dimensional dynamical systems. J Dynam Differ Equations 3: 471-513
17. Sacker RJ, Sell GR (1994) Dichotomies for linear evolutionary equations in Banach spaces. J Differ Equations 113: 17-67