The existence and multiplicity of periodic solutions are obtained for the nonau-Ž . tonomous second order systems with locally coercive potential; that is, F t, x ª < < w x qϱ as x ª ϱ 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. ᮊ

Some existence theorems are obtained by the least action principle for periodic solutions of nonautonomous second-order systems with a potential which is the sum of a subconvex function and a subquadratic function.

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