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

Zhihua Liu, Pierre Magal, Shigui Ruan

Research output: Contribution to journalArticle

16 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1784-1809
Number of pages26
JournalJournal of Differential Equations
Volume244
Issue number7
DOIs
StatePublished - Apr 1 2008

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Keywords

  • Functional differential equations
  • Hille-Yosida operator
  • Integrated semigroup
  • Projectors
  • Semi-linear problem
  • Spectrum

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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