New Periodic Solutions for the Singular Hamiltonian System

By use of the Cerami-Palais-Smale condition, we generalize the classical Weierstrass minimizing theorem to the singular case by allowing functions which attain infinity at some values. As an application, we study certain singular second-order Hamiltonian systems with strong force potential at the origin and show the existence of new periodic solutions with fixed periods.

Existence of Solutions for Some Classes of Singular Hamiltonian Systems

This paper deals with existence of positive solution for the following singular Hamiltonian systemwhere Ω ⊂ ℝ