Nonconstant periodic solutions with any fixed energy for singular Hamiltonian systems

Abstract

In the past years, there were very few works on the existence of nonconstant periodic solutions with fixed energy of singular second-order Hamiltonian systems, and now we attempt to ingeniously use Ekeland's variational principle to prove the existence of nonconstant periodic solutions with any fixed energy for singular second-order Hamiltonian systems, and our results greatly generalize some well known results such as [1, Theorem 3.6]. Moreover, we exhibit two simple and instructive singular potential examples to make our result more clear, which have not been solved by known results.