PERIODIC SOLUTIONS FOR A TYPE OF NEUTRAL SYSTEM WITH VARIABLE PARAMETERS

Abstract

In this paper, we firstly analyze some properties of the linear difference operator[<i>Ax</i>](<i>t</i>)=<i>x</i>(<i>t</i>) -<i>C</i>(<i>t</i>)<i>x</i>(<i>t</i> -<i>τ</i>),where <i>C</i>(<i>t</i>) is a <i>n</i>&#215;<i>n</i> matrix function, and then using Mawhin's continuation theorem, a first-order neutral functional differential system is studied. Some new results on the existence and stability of periodic solutions are obtained. The results are related to the deviating arguments <i>τ</i> and <i>µ</i>. Meanwhile, the approaches to estimate a prior bounds of periodic solutions are different from the corresponding ones of the known literature.