Multiple Solutions in Systems of Functional Differential Equations

d'Albis, Hippolyte and Augeraud-Véron, Emmanuelle and Hupkes, Herman Jan (2014): Multiple Solutions in Systems of Functional Differential Equations. Forthcoming in: Journal of Mathematical Economics

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Delay Differential Equations, Advance Differential Equations, Existence, Indeterminacy
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; E - Macroeconomics and Monetary Economics > E1 - General Aggregative Models > E13 - Neoclassical

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