On a class of differential-algebraic equations with infinite delay

Abstract

We study the set of $T$-periodic solutions of a class of $T$-periodically perturbed Differential-Algebraic Equations, allowing the perturbation to contain a distributed and possibly infinite delay. Under suitable assumptions, the perturbed equations are equivalent to Retarded Functional (Ordinary) Differential Equations on a manifold. Our study is based on known results about the latter class of equations and on a ``reduction'' formula for the degree of a tangent vector field to implicitly defined differentiable manifolds.

Keywords

• differential-algebraic equations
• retarded functional equations
• periodic solution
• periodic perturbation
• infinite delay