Geodesic
Closed semistable operators and singular differential equations
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 605-620

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which $0$ is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of $C_0$-semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly perturbed differential equation in a Banach space.
Classification : 34G10, 47A10, 47A60, 47D06
Keywords: closed linear operator; $C_0$-semigroup; infinitesimal generator; semistable operator; singular differential equation 
@article{CMJ_2003__53_3_a8,
     author = {Koliha, J. J. and Tran, Trung Dinh},
     title = {Closed semistable operators and singular differential equations},
     journal = {Czechoslovak Mathematical Journal},
     pages = {605--620},
     publisher = {mathdoc},
     volume = {53},
     number = {3},
     year = {2003},
     mrnumber = {2000056},
     zbl = {1080.47500},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2003__53_3_a8/}
}
TY  - JOUR
AU  - Koliha, J. J.
AU  - Tran, Trung Dinh
TI  - Closed semistable operators and singular differential equations
JO  - Czechoslovak Mathematical Journal
PY  - 2003
SP  - 605
EP  - 620
VL  - 53
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMJ_2003__53_3_a8/
LA  - en
ID  - CMJ_2003__53_3_a8
ER  - 
%0 Journal Article
%A Koliha, J. J.
%A Tran, Trung Dinh
%T Closed semistable operators and singular differential equations
%J Czechoslovak Mathematical Journal
%D 2003
%P 605-620
%V 53
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMJ_2003__53_3_a8/
%G en
%F CMJ_2003__53_3_a8
Koliha, J. J.; Tran, Trung Dinh. Closed semistable operators and singular differential equations. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 605-620. http://geodesic.mathdoc.fr/item/CMJ_2003__53_3_a8/