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Poincaré–Birkhoff results for Lagrangian systems with subquadratic potential

Published online by Cambridge University Press:  14 November 2011

Silvia Cingolani  and
Lorenzo Pisani
Silvia Cingolani
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari, Campus Universitario, via E. Orabona, 4, 70125 Bari, Italy
Lorenzo Pisani
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari, Campus Universitario, via E. Orabona, 4, 70125 Bari, Italy
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Abstract

In this paper, using a recent generalisation of Morse Theory, we study the existence of periodic solutions of the Lagrangian equation (1.1) with subquadratic potential and asymptotically flat, nonconstant, time-dependent metric on ℝN. In Section 3, we get also an ‘alternative result’ about the minimal period or the existence of infinitely many solutions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 6 , 1995 , pp. 1169 - 1177
Copyright
Copyright © Royal Society of Edinburgh 1995

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