Geodesic
Harmonic solutions to a class of differential-algebraic equations with separated variables
Electronic journal of differential equations, Tome 2012 (2012)
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.
Classification : 34A09, 34C25, 34C40
Keywords: differential-algebraic equations, periodic solutions, ordinary differential equations on manifolds, degree of a vector field 
@article{EJDE_2012__2012__a23,
     author = {Bisconti,  Luca},
     title = {Harmonic solutions to a class of differential-algebraic equations with separated variables},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1242.34016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a23/}
}
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Bisconti,  Luca. Harmonic solutions to a class of differential-algebraic equations with separated variables. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a23/