## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Theorems of Perron type for uniform exponential dichotomy of linear skew-product semiflows.

#### Abstract

We study the connections between the uniform exponential dichotomy of a discrete linear skew-product semiflow and the uniform admissibility of the pair $(c_{0}(\n,X),c_{00}(\n, X))$. We give necessary and sufficient conditions for uniform exponential dichotomy of linear skew-product semiflows in terms of the uniform admissibility of the pairs $(c_{0}(\n, X),c_{00}(\n, X))$ and $(C_0(\r, X),$ $C_{00}(\r, X))$, respectively. We generalize a dichotomy theorem due to Van Minh, Räbiger and Schnaubelt for the case of linear skew-product semiflows.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 1 (2003), 1-21.

Dates
First available in Project Euclid: 10 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1047309409

Digital Object Identifier
doi:10.36045/bbms/1047309409

Mathematical Reviews number (MathSciNet)
MR2032321

Zentralblatt MATH identifier
1045.34022

#### Citation

Megan, Mihail; Sasu, Adina Luminiţa; Sasu, Bogdan. Theorems of Perron type for uniform exponential dichotomy of linear skew-product semiflows. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), no. 1, 1--21. doi:10.36045/bbms/1047309409. https://projecteuclid.org/euclid.bbms/1047309409