On Well-Posedness of Singular Neutral Equations in the State Space C

Authors: Ito K.¹; Kappel F.²; Turi J.³

Source: Journal of Differential Equations, Volume 125, Number 1, February 1996 , pp. 40-72(33)

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Abstract:

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 space C (- 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.

Language: English

Document Type: Research article

Affiliations: 1: Department of Mathematics, North Carolina State University, Raleigh, North Carolina, 27695 2: Institut fur Mathematik, Universitat Graz, Heinrichstrasse 36, Graz, A-8010, Austria 3: Programs in Mathematical Sciences, University of Texas at Dallas, Richardson, Texas, 75083-0688

Publication date: 1996-02-01