Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 02, pp. 1-15.

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

Author: Luca Bisconti (Univ. di Firenze, Italy)

Abstract: 
  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 02, 2012.
Math Subject Classifications: 34A09, 34C25, 34C40.
Key Words: Differential-algebraic equations; periodic  solutions;
           ordinary differential  equations on manifolds;
           degree of a vector field.