The problem of existence of periodic solutions for neutral functional differential system with nonlinear difference operator

In this paper, the authors investigate some new properties of nonlinear difference operator in the first, which is associated with neutral functional differential equations. Then, by using these new properties, the problem of existence of periodic solutions for neutral functional differential system with nonlinear operator D 1 ( φ ) = φ ( 0 ) − B φ ( − τ ) − h ( φ ) is studied. The interesting thing is that the periodic solution to the system is allowed to be not differentiable.