Electron. J. Diff. Equ., Vol. 2012 (2012), No. 02, pp. 1-15.

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

Luca Bisconti

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.

Show me the PDF file (307 KB), TEX file, and other files for this article.

Luca Bisconti
Dipartimento di Sistemi e Informatica
Universitá di Firenze
Via Santa Marta 3, 50139 Firenze, Italy
email: luca.bisconti@unifi.it

Return to the EJDE web page