 
Summary: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 165, 71101 (1992)
Asymptotic Integration
of Delay Differential Systems
SHANGBING AI
Department of Mathematics, Shandong University,
Jinan, Shandong 250100, People's Republic of China
1. INTRODUCTION
The purpose of this paper is to completely prove a conjecture in J. R.
Haddock and R. Sacker [l] and further extend a result on asymptotic
integration obtained previously by 0. Arino and I. Gyori [24].
Asymptotic integration deals with nonautonomous evolution equations
which asymptotically are autonomous, and aims at relating the asymptotic
behavior of the solutions of these equations to the asymptotic behavior of
the solutions of the limit equation. Classical results on this problem exist
for ordinary differential equations (i.e., cf. [591). For delay differential
equations, the earliest results are due to K. L. Cooke [lo], and somelater
results can be found in [l4, 11&16].
In [ 11, in search of an extension of results by Hartman [S], Hartman
and Wintner [6], Atkinson [7], and Harris and Lutz [S], notably for
ordinary differential equations of the form
