Abstract
In this paper, we analyze some properties of the linear difference operator A: C T → C T , [Ax](t)=x(t)−V(t)x(t−τ), and then, by using the coincidence degree theory of Mawhin, a kind of neutral differential systems with non-constant matrix is studied. Some new results on the existence of periodicity are obtained. It is worth noting that V(t) is no longer a constant matrix, which is different from the corresponding ones of past work.
Highlights
The field of neutral functional equations is making significant breakthroughs in its practice; it is no longer only a specialist’s field
In the last few years, the stability of neutral systems of various classes with time delays has received an ever-growing interest from many authors
It is well known that the existence of periodic solutions of neutral equations and neutral systems is a very basic and important problem, which plays a role similar to stability
Summary
The field of neutral functional equations (in short NFDEs) is making significant breakthroughs in its practice; it is no longer only a specialist’s field. Qualitative analysis such as periodicity and stability of solutions of NFDEs has been studied extensively by many authors. We refer to [ – ] for some recent work on the subject of periodicity and stability of neutral equations.
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