Viability for Semilinear Differential Equations with Infinite Delay

Qixiang Dong and Gang Li
Additional contact information
Qixiang Dong: School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
Gang Li: School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China

Mathematics, 2016, vol. 4, issue 4, 1-11

Abstract: Let X be a Banach space, A : D ( A ) ? X ? X the generator of a compact C 0 -semigroup S ( t ) : X ? X , t ? 0 , D ( · ) : ( a , b ) ? 2 X a tube in X , and f : ( a , b ) × B ? X a function of Carathéodory type. The main result of this paper is that a necessary and sufficient condition in order that D ( · ) be viable of the semilinear differential equation with infinite delay u ? ( t ) = A u ( t ) + f ( t , u t ) , t ? [ t 0 , t 0 + T ] , u t 0 = ? ? B is the tangency condition lim inf h ? 0 h ? 1 d ( S ( h ) v ( 0 ) + h f ( t , v ) ; D ( t + h ) ) = 0 for almost every t ? ( a , b ) and every v ? B with v ( 0 ) ? D ( t ) .

Keywords: viable domain; differential equation; infinite delay; tangency condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/4/4/64/pdf (application/pdf)
https://www.mdpi.com/2227-7390/4/4/64/ (text/html)

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:gam:jmathe:v:4:y:2016:i:4:p:64-:d:82323

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().