On a class of differential-algebraic equations with infinite delay

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 as- sumptions, the perturbed equations are equivalent to Retarded Func- tional (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 implic- itly defined differentiable manifolds.