Electron. J. Diff. Eqns., Vol. 2007(2007), No. 62, pp. 1-5.

Forced oscillations for delay motion equations on manifolds

Pierluigi Benevieri, Alessandro Calamai,
Massimo Furi, Maria Patrizia Pera

Abstract:
We prove an existence result for $T$-periodic solutions of a $T$-periodic second order delay differential equation on a boundaryless compact manifold with nonzero Euler-Poincare characteristic. The approach is based on an existence result recently obtained by the authors for first order delay differential equations on compact manifolds with boundary.

Submitted July 29, 2006. Published April 26, 2007.
Math Subject Classifications: 34K13, 37C25.
Key Words: Delay differential equations; Forced oscillations; periodic solutions; compact manifolds; Euler-Poincare characteristic; fixed point index.

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Pierluigi Benevieri
Dipartimento di Matematica Applicata "Giovanni Sansone"
Università degli Studi di Firenze
Via S. Marta 3, I-50139 Firenze, Italy
email: pierluigi.benevieri@unifi.it
Alessandro Calamai
Dipartimento di Scienze Matematiche
Università Politecnica delle Marche
Via Brecce Bianche, I-60131 Ancona, Italy
email: calamai@math.unifi.it, calamai@dipmat.univpm.it
Massimo Furi
Dipartimento di Matematica Applicata "Giovanni Sansone"
Università degli Studi di Firenze
Via S. Marta 3, I-50139 Firenze, Italy
email: massimo.furi@unifi.it
Maria Patrizia Pera
Dipartimento di Matematica Applicata "Giovanni Sansone"
Università degli Studi di Firenze
Via S. Marta 3, I-50139 Firenze, Italy
email: mpatrizia.pera@unifi.it

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