Projectors on the generalized eigenspaces for functional differential equations using integrated semigroups

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:244

Article

Liu, Zhihua^2,3  Magal, Pierre²  Ruan, Shigui¹ 

[1] Univ Miami, Dept Math, Coral Gables, FL 33124 USA

[2] Univ Havre, Fac Sci & Tech, F-76058 Le Havre, France

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

关键词: functional differential equations;    semi-linear problem;    integrated semigroup;    Hille-Yosida operator;    spectrum;    projectors;   

DOI  :  10.1016/j.jde.2008.01.007

来源: Elsevier

【 摘 要 】

The aim of this article is to derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues for linear functional differential equations (FDE) by using integrated semigroup theory. The idea is to formulate the FDE as a non-densely defined Cauchy problem and obtain an explicit formula for the integrated solutions of the non-densely defined Cauchy problem, from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated to some eigenvalues. The results are useful in studying bifurcations in some semi-linear problems. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free