Non-collision periodic solutions of forced dynamical systems with weak singularities

Pedro J. Torres

doi:10.3934/dcds.2004.11.693

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2004, Volume 11, Issue 2&3: 693-698. Doi: 10.3934/dcds.2004.11.693

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Non-collision periodic solutions of forced dynamical systems with weak singularities

Pedro J. Torres^1,

1.
Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada Campus de Fuentenueva s/n, 18071 Granada

Received: March 31, 2003

Revised: February 29, 2004

Published: August 2004

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Abstract

We prove the existence of periodic solutions in a second order differential system with a singular potential of attractive or repulsive type and forced periodically. The proof is based on a Krasnoselskii fixed point theorem for absolutely continuous operators on a Banach space, and this makes possible to avoid any kind of "strong force" condition.

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Mathematics Subject Classification: 34C25.

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