Periodic Solutions for Second Order Systems with Not Uniformly Coercive Potential1

The existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential; that is, FŽt, x. as x for a.e. t in some positive-measure subset of 0, T , by using an analogy of Egorov’s Theorem, the properties of subadditive functions, the least action principle, and a three-critical-point theorem proposed by Brezis and Niren - berg.