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March  2004, 11(2&3): 693-698. doi: 10.3934/dcds.2004.11.693

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, Spain

Received  April 2003 Revised  March 2004 Published  June 2004

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.
Keywords: weak singularity., Periodic solution, singular potential.
Mathematics Subject Classification: 34C2.
Citation: Pedro J. Torres. Non-collision periodic solutions of forced dynamical systems with weak singularities. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 693-698. doi: 10.3934/dcds.2004.11.693
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