Periodic solutions for second order systems with not uniformly coercive potential

The existence and multiplicity of periodic solutions are obtained for the nonautonomous second order systems with locally coercive potential; that is, F(t, x) --> +infinity as \x\ --> infinity 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 Nirenberg. (C) 2001 Academic Press.