一类二阶非线性微分方程组的周期解

Periodic solutions for a class of second order nonlinear differential equations

用单调迭代法给出二阶非线性微分方程组x″i(t) +fi(x1 ,… ,xn,t) =0 ,i=1 ,2 ,… ,n(其中 fi(x1 ,… ,xn,t) :Rn×R→R连续 )存在周期解的充分条件。

Using iterative method to study the existence of periodic solutions of the following equations: x ″ i(t)+f i(x 1,...,x n,t)=0,i=1,2,...,n (where f i(x 1,...,x n,t):R n×R→R continuous). Sufficient conditions for the equations to have an odd periodic solution are given.