Some results on solutions of minimal period to superquadratic Hamiltonian systems

Then, it is well known that Rabinowitz’s theorem (see [8]) guarantees the existence, for every T > 0, of at least one nontrivial solution to (l), but he left open the question to find a solution having minimal period T. When H is convex, some results have been recently obtained about such a problem via duality methods. The problem has been completely solved by Ambrosetti & Mancini (see [2,7]), with a suitable hypothesis on the second derivative of H, and by Clarke & Ekeland (see [4]), replacing (Hj), (HA) and (H5) with a subquadratic hypothesis. In another framework, Rabinowitz determines in [9] a family of solutions to (l), having minimal periods which diverge, in the superquadratic case (see theorem 2.34) under the