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Connecting orbits for a class of singular time-periodic second-order Hamiltonian systems

Part of: Qualitative theory Variational problems in infinite-dimensional spaces

Published online by Cambridge University Press:  08 November 2016

Hossein Tehrani
Hossein Tehrani*
Affiliation:
Department of Mathematical Sciences, University of Nevada Las Vegas, Box 454020, Las Vegas, NV 89154-4020, USA (tehranih@unlv.nevada.edu)
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We show the existence of connecting orbits for a class of singular second-order Hamiltonian systems

where, as opposed to most of the existing literature, we assume that the potential V has not one but any finite number of maxima of equal value. We use variational methods under the assumption that V (t, u) satisfies the so-called ‘strong-force’ condition at the singularity.

Keywords

singular Hamiltonian systemhomoclinicheteroclinic solutionsstrong-force conditionconcentration compactnessLusternik–Schnirelmann category

MSC classification

Secondary: 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel'man) theory, etc.) 34C25: Periodic solutions
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 6 , December 2016 , pp. 1211 - 1241
Copyright
Copyright © Royal Society of Edinburgh 2016