Multiple solutions in systems of functional differential equations

Hippolyte d'Albis (1) , Emmanuelle Augeraud-Véron (2) , Hermen Jan Hupkes (3)

1 CES - Centre d'économie de la Sorbonne
2 MIA - Mathématiques, Image et Applications - EA 3165
3 Mathematical institute

This paper proposes conditions for the existence and uniqueness of solutions to systems of linear differential or algebraic equations with delays or advances, in which some variables may be non-predetermined. These conditions represent the counterpart to the Blanchard and Kahn conditions for the functional equations under consideration. To illustrate the mathematical results, applications to an overlapping generations model and a time-to-build model are developed.

Mots clés: Delay differential equations; Advance differential equations; Existence; Indeterminacy

Domaines: Economies et finances

Hippolyte d'Albis, Emmanuelle Augeraud-Véron, Hermen Jan Hupkes. Multiple solutions in systems of functional differential equations. Journal of Mathematical Economics, 2014, 52, pp.50-56. ⟨10.1016/j.jmateco.2014.03.010⟩. ⟨hal-01015386⟩