On Well-Posedness of Singular Neutral Equations in the State SpaceC

In this paper we study necessary und sufficient conditions for well-posedness of scalar, singular (i.e., with a difference operator which is nonatomic at zero) neutral functional differential equations (SNFDEs) in the state spaceC(−r, 0). We also discuss an ill-posed SNFDE in order to illustrate how the addition of a singularity away from zero (in our case we have a perturbing atom at −r) can destroy well-posedness.