Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 4, Number 3 (1999), 169-194.
Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations
We investigate the asymptotic properties of the inhomogeneous nonautonomous evolution equation , where is a Hille-Yosida operator on a Banach space , is a family of operators in satisfying certain boundedness and measurability conditions and . The solutions of the corresponding homogeneous equations are represented by an evolution family . For various function spaces we show conditions on and which ensure the existence of a unique solution contained in . In particular, if is -periodic there exists a unique bounded solution subject to certain spectral assumptions on and . We apply the results to nonautonomous semilinear retarded differential equations. For certain -periodic retarded differential equations we derive a characteristic equation which is used to determine the spectrum of .
Abstr. Appl. Anal., Volume 4, Number 3 (1999), 169-194.
First available in Project Euclid: 9 April 2003
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Gühring, Gabriele; Räbiger, Frank. Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations. Abstr. Appl. Anal. 4 (1999), no. 3, 169--194. doi:10.1155/S1085337599000214. https://projecteuclid.org/euclid.aaa/1049907202