Differential and Integral Equations

Special solutions for linear functional differential equations and asymptotic behaviour

Abstract

The present paper deals with special solutions for linear functional differential equations with small delays. The importance of special solutions relies on the fact that, under some conditions, they can be used to describe the asymptotic behaviour of all solutions. Sufficient conditions for the existence of special solutions for nonautonomous equations in $\mathbb R^n$ are given. For autonomous equations in $\mathbb R^n$, results relating special solutions and characteristic values are presented. We also consider linear autonomous functional differential equations in Banach spaces, and use special solutions to study the asymptotic behaviour of their solutions. Several applications are given.

Article information

Source
Differential Integral Equations, Volume 18, Number 3 (2005), 337-360.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060223

Mathematical Reviews number (MathSciNet)
MR2122724

Zentralblatt MATH identifier
1212.34233

Subjects
Primary: 34K06: Linear functional-differential equations
Secondary: 34K12: Growth, boundedness, comparison of solutions

Citation

Faria, Teresa; Huang, Wenzhang. Special solutions for linear functional differential equations and asymptotic behaviour. Differential Integral Equations 18 (2005), no. 3, 337--360. https://projecteuclid.org/euclid.die/1356060223