Abstract:

The purpose of this paper is to study the existence of periodic solutions of the following second order systems by the
critical point theory. When the nonlinear term F(t,x)=F1(t,x)+F2(x) satisfies assumption（A）, and F1(t,x),F2(x) satisfy many boundary conditions, one new existence theorem is obtained by the least action principle.

Key words: periodic solutions, the least action principle, second order systems