Harmonic solutions to a class of differential-algebraic equations with separated variables

2011/10/09 by Luca Bisconti, Bisconti, Luca
Mathematics · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CA #math.DS

paper · pdf · doi:10.48550/arxiv.1110.1833

arxiv created 2011/12/22 · arxiv updated 2011/12/23

Abstract

We study the set of T-periodic solutions of a class of T-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.

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