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Multiplicity of homoclinic solutions for singular second-order conservative systems

Published online by Cambridge University Press:  14 November 2011

Maria Letizia Bertotti  and
Louis Jeanjean
Maria Letizia Bertotti
Affiliation:
Laboratorio di Matematica Applicata, Ingegneria, Università degli Studi di Trento, 38050 Trento, Italy e-mail: MariaLetizia.Bertotti@ing.unitn.it
Louis Jeanjean
Affiliation:
Equipe d'Analyse et de Mathématiques Appliquées, Université de Marne la Vallée, 93166 Noisy le Grand Cedex, France e-mail: Jeanjean@math.univ.mlv.fr
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Abstract

We consider a class of second-order systems , with q(t) ∊ℝn, for which the potential energy V: ℝn\S→ℝ admits a (possibly unbounded) singular set S ⊂ℝn and has a unique absolute maximum at 0 ∈ℝn. Under some conditions on S and V, we prove the existence of several solutions homoclinic to 0.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 126 , Issue 6 , 1996 , pp. 1169 - 1180
Copyright
Copyright © Royal Society of Edinburgh 1996

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