LAGRANGIAN SYSTEMS IN THE PRESENCE OF SINGULARITIES

Many authors have studied this problem in the case when fi = R^ (so dQ = 0)under various assumptions on the growth of V(t,q) as \q\ —► oo: cf., for instance,[2, 3, 5, 9, 10]. W. B. Gordon was the first to study our case by means of variationalmethods, and we refer to [6, 7] for the physical motivation of the problem (cf. alsothe end of this section). Finally we refer to [1, 8] for the case V(t,q) —► +oo as