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Proceedings of the American Mathematical Society

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On periodic solutions of autonomous Hamiltonian systems of ordinary differential equations

Author: David C. Clark
Journal: Proc. Amer. Math. Soc. 39 (1973), 579-584
MSC: Primary 34C25
MathSciNet review: 0315217
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Abstract: For the system $ x''(t) + \operatorname{grad} U(x(t)) = 0$ lower bounds are obtained for the number of pairs $ \pm x(t)$ of odd, periodic solutions, with the period prescribed. These bounds are in terms of the behavior of $ U(x)$ near the origin and far away from the origin. It is assumed that $ U(x)$ is even, and two different types of behavior of $ U(x)$ far away from the origin are considered.

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Keywords: Periodic solutions, Hamiltonian systems, Lusternik-Schnirelman theory, Palais-Smale condition, index of quadratic form
Article copyright: © Copyright 1973 American Mathematical Society