Periodic solutions of linear neutral integrodifferential equations (Q2266370)

The paper discusses the linear neutral integrodifferential equations \[ (d/dt)(y(t)-\int^{t}_{0}D(t-s)y(s)ds)=Ay(t)+\int^{t}_{0}C(t- s)y(s)ds+f(t),and \] \[ (d/dt)(x(t)-\int^{t}_{-\infty}D(t- s)x(s)ds)=Ax(t)+\int^{t}_{-\infty}C(t-s)x(s)ds+f(t), \] where \(x,y\in R^ n\), A is an \(n\times n\) constant matrix, C,D are \(n\times n\) matrices of continuous functions, and f: (-\(\infty,\infty)\to R^ n\) is continuous. The aim of the paper is to get a nice formula for periodic solutions to these equations. As a corollary to our results, the corresponding theorem of \textit{T. A. Burton} [Funkc. Ekvacioj, Ser. Int. 27, 229-254 (1984)] is included.