We study the properties of periodic solutions of a class of periodically perturbed Differential-Algebraic Equations with separated variables. Under suitable hypotheses, these equations are equivalent to separated variables ODEs on a manifold. By combining known results on Differential-Algebraic Equations, with an argument about ODEs on manifolds, we obtain a global continuation result for the T-periodic solutions to the considered equations. As an application of our method, a multiplicity result is provided.
Submitted December 2, 2011. Published January 2, 2012.
Math Subject Classifications: 34A09, 34C25, 34C40.
Key Words: Differential-algebraic equations; periodic solutions; ordinary differential equations on manifolds; degree of a vector field.
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| Luca Bisconti |
Dipartimento di Sistemi e Informatica
Universitá di Firenze
Via Santa Marta 3, 50139 Firenze, Italy
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