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Stability and determinacy conditions for mixed-type functional differential equations
Institution:1. Paris School of Economics - University Paris 1, CES, 106 bd de l’Hopital, 75013, Paris, France;2. University of La Rochelle (MIA), Avenue Michel Crepeau, 47042, La Rochelle, France;3. University of Leiden, P.O. Box 9512, 2300 RA Leiden, The Netherlands;1. Center for Mathematical Economics, Universität Bielefeld Postfach 10 01 31 D-33501 Bielefeld, Germany;2. University of Johannesburg, South Africa;3. Paris School of Economics, CNRS, France;4. Paris School of Economics, University of Paris 1 Panthéon-Sorbonne, France;1. CNRS (LEM, UMR 8179), France;2. Iéseg School of Management, 3 rue de la Digue, 59000 Lille, France;3. CORE (Université Catholique de Louvain), 34 voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium;4. EM Lyon Business School, 23 avenue Guy de Collongue, 69134 Ecully Cedex, France;1. Department of Economics, Yokohama National University, 79-3 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan;2. Faculty of Economics, Fukuoka University, 8-19-1 Nanakuma, Jonan-ku, Fukuoka 814-0180, Japan
Abstract:This paper analyzes the solution of linear mixed-type functional differential equations with either predetermined or non-predetermined variables. Conditions characterizing the existence and uniqueness of a solution are given and related to the local stability and determinacy properties of the steady state. In particular, it is shown that the relationship between the uniqueness of the solution and the stability of the steady-state is more subtle than the one that holds for ordinary differential equations, and gives rise to new dynamic configurations.
Keywords:Functional differential equations  Local dynamics  Existence  Determinacy
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