Exponential stability for abstract linear autonomous functional differential equations with infinite delay

Jin Liang, Falun Huang and Tijun Xiao

International Journal of Mathematics and Mathematical Sciences, 1998, vol. 21, 1-5

Abstract:

Based on our preceding paper, this note is concerned with the exponential stability of the solution semigroup for the abstract linear autonomous functional differential equation x ˙ ( t ) = L ( x t ) ( ∗ ) where L is a continuous linear operator on some abstract phase space B into a Banach space E . We prove that the solution semigroup of ( ∗ ) is exponentially stable if and only if the fundamental operator ( ∗ ) is exponentially stable and the phase space B is an exponentially fading memory space.

Date: 1998
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/21/549151.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/21/549151.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:549151

DOI: 10.1155/S0161171298000362

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().