Abstract
The exponential stability property of an evolutionary process is characterized in terms of the existence of some functionals on certain function spaces. Thus are generalized some well-known results obtained by Datko, Rolewicz, Littman and Van Neerven.
Similar content being viewed by others
References
R. Datko: Extending a theorem of Liapunov to Hilbert spaces. J. Math. Anal. Appl. 32 (1970), 610–616.
R. Datko: Uniform asymptotic stability of evolutionary processes in a Banach space. SIAM. J. Math. Analysis 3 (1973), 428–445.
E. Hille and R. S. Phillips: Functional Analysis and Semi-groups (revised edition). Amer. Math. Soc. Colloq. Publ. Vol. 31, Providence, R.I., 1957.
W. Littman: A generalization of the theorem Datko-Pazy. Lecture Notes in Control and Inform. Sci., Springer Verlag 130 (1989), 318–323.
J. M. A. M. van Neerven: Exponential stability of operators and semigroups. J. Func. Anal. 130 (1995), 293–309.
J. M. A. M. van Neerven: The Asymptotic Behaviour of Semigroups of Linear Operators, Theory, Advances and Applications, Vol. 88. Birkhauser, 1996.
J. M. A. M. van Neerven: Lower semicontinuity and the theorem of Datko and Pazy. Int. Eq. Op. Theory 42 (2002), 482–492.
A. Pazy: On the applicability of Liapunov’s theorem in Hilbert spaces. SIAM. J. Math. Anal. Appl. 3 (1972), 291–294.
A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations. Springer-Verlag, 1983.
S. Rolewicz: On uniform N-equistability. J. Math. Anal. Appl. 115 (1986), 434–441.
J. Zabczyk: Remarks on the control of discrete-time distributed parameter systems. SIAM J. Control. Optim. 12 (1974), 721–735.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Preda, P., Pogan, A. & Preda, C. Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes. Czech Math J 56, 425–435 (2006). https://doi.org/10.1007/s10587-006-0028-2
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10587-006-0028-2