Periodic Solutions of Lagrangian Systems on a Compact Manifold

摘要

The question of existence and the number of periodic solutions of model equations for a classical mechanical system is a problem as old as the field of analytical mechanics itself. The development of the nonlinear functional analysis has renewed interest in these problems. In this paper we consider a mechanical system which is constrained to a compact manifold M. We suppose that the dynamics of the system is described by a T-periodic Lagrangian L sub t: TM approaches R which satisfies reasonable physical assumptions. The main result of this paper is: If the fundamental group of the manifold M is finite, then the Lagrangian nonlinear system of differential equations which describes the dynamical system has infinitely many distinct periodic solutions. (Author)