Notes on a Theorem of Benci-Gluck-Ziller-Hayashi

Abstract

We use constrained variational minimizing methods to study the existence of periodic solutions with a prescribed energy for a class of second order Hamiltonian systems with a $C^2$ potential function which may have an unbounded potential well. Our result can be regarded as complementary to the well-known theorem of Benci-Gluck-Ziller and Hayashi.