关于非自治Lagrange系统的周期解

on periodic solutions of nonautonomous lagrangian systems

用变分方法研究非自治 L agrange系统周期解的问题转化为研究 L agrange作用泛函的临界点问题 .对 L agrange系统 ,人们用变分方法已经获得了一系列可解性条件 ,但是除在超二次条件下 ,Lagrange作用泛函都是下方有界的 .这里的目的是给出 Lagrange作用泛函无界的 L agrange系统周期解的其它可解性条件 .这时的主要困难是对应的 L agrange作用泛函不再是下方有界的 .这里用临界点理论中的鞍点定理得到了

the periodic solutions of nonautonomous Lagrangian systemsare equivalent to critical points of lagrangian action funct Ionalby the variation methods. For lagrangian systems, some solvability conditio Ns, are obtained by the variation mehtods. But the lagrangian action functional Are all bounded below except for the case under the superquadratic condition. Th E purpose of this paper is giving other solvability condition of lagrangian syst Ems with unbounded lagrangian action functional. The main difficulty is unbounde Dness of lagrangian action functional. In this paper, under condition that m sat Isfying some suitable conditions and v satisfying that the existence is obtained for periodic solutions of lagrangian systems by the saddle point theorem in cri Tical point theory.=