Multi Point Boundary Value Problems for Second Order Differential Inclusions
Since the mid-nineties it has gradually become understood that the Cartan prolongation of rank 2 distributions is a key operation leading locally, when applied many times, to all so-called Goursat distributions. That is those, whose derived flag of consecutive Lie squares is a 1-flag (growing in ranks always by 1). We first observe that successive generalized Cartan prolongations (gCp) of rank k + 1 distributions lead locally to all special k-flags: rank k + 1 distributions D with the derived...
In this Note we prove the existence of infinitely many periodic solutions of prescribed period for a Hamiltonian system with a singular potential.