In this paper we investigate the properties of the set of T-periodic solutions of semi-explicit parametrized differential-algebraic equations with non-autonomous constraints of a particular type. We provide simple, degree-theoretic conditions for the existence of branches of T-periodic solutions of the considered equations. Our approach is based on topological arguments as regards differential equations on implicitly defined manifolds, combined with elementary facts of matrix analysis. MSC:34A09, 34C25, 34C40.
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