Essential growth rate for bounded linear perturbation of non-densely defined Cauchy problems

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:341

Article

Ducrot, A.²  Liu, Z.^1,3,4  Magal, P.^1,3 

[1] Univ Le Havre, LMAH, F-100875 Le Havre, France

[2] Univ Bordeaux 2, CNRS, UMR 5466 MAB, F-33076 Bordeaux, France

[3] Univ Bordeaux 2, INRIA Futurs Anubis, F-33076 Bordeaux, France

[4] Beijing Normal Univ, Dept Math, Beijing 100875, Peoples R China

关键词: semigroups;    integrated semigroups;    essential growth rate;    bounded perturbation;    non-densely defined operators;   

DOI  :  10.1016/j.jmaa.2007.09.074

来源: Elsevier

【 摘 要 】

This paper is devoted to the study of the essential growth rate of some class of semigroup generated by bounded perturbation of some non-densely defined problem. We extend some previous results due to Thieme [H.R. Thieme, Quasi-compact semigroups via bounded perturbation, in: Advances in Mathematical Population Dynamics-Molecules, Cells and Man, Houston, TX, 1995, in: Ser. Math. Biol. Med., vol. 6, World Sci. Publishing, River Edge, NJ, 1997, pp. 691-711] to a class of non-densely defined Cauchy problems in LP. In particular in the context the integrated semigroup is not operator norm locally Lipschitz continuous. We overcome the lack of Lipschitz continuity of the integrated semigroup by deriving some weaker properties that are sufficient to give information on the essential growth rate. (C) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

Free