Applications of Natural Constraints in Critical Point Theory to Periodic Solutions of Natural Hamiltonian Systems.

摘要

This paper deals with periodic solutions of Hamiltonian systems of the form -x = V'(x) with V a given function. Assuming V to be either a convex or an even function, and prescribing the period, existence results are obtained for the number of solutions in relation to the minimal period of these solutions, assuming superquadratic growth at infinity only, or subquadratic growth at infinity together with specific behaviour at the origin for V. By introducing natural constraints, these results are obtained by applying variational methods directly to the action functional. (Author)