Next Article in Journal
Some Determinantal Expressions and Recurrence Relations of the Bernoulli Polynomials
Previous Article in Journal
Positive Solutions for Nonlinear Caputo Type Fractional q-Difference Equations with Integral Boundary Conditions
Article Menu

Export Article

Open AccessArticle
Mathematics 2016, 4(4), 64; doi:10.3390/math4040064

Viability for Semilinear Differential Equations with Infinite Delay

†,* and
School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Academic Editor: Johnny Henderson
Received: 1 September 2016 / Revised: 25 October 2016 / Accepted: 2 November 2016 / Published: 8 November 2016
View Full-Text   |   Download PDF [265 KB, uploaded 8 November 2016]

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 = ϕ 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 ) . View Full-Text
Keywords: viable domain; differential equation; infinite delay; tangency condition viable domain; differential equation; infinite delay; tangency condition
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Dong, Q.; Li, G. Viability for Semilinear Differential Equations with Infinite Delay. Mathematics 2016, 4, 64.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top