中文摘要：

利用主积分方法,将周期系统平衡点的稳定性判据推广到拟周期情形,即证明拟周期二阶微分方程x″＋h（t）x′＋a（t）x2n＋1＋e（t,x）=0（n≥1）平衡点x=x′=0的稳定性,其中h（t）,a（t）,e（t,x）是拟周期系数,其频率向量满足Diophantine条件,且在x=x′=0附近,｜e（t,x）｜=O（x2n＋2）.结果表明,具有变号阻尼项拟周期振子的平衡点在一定条件下具有稳定性.

英文摘要：

We generalized the stability criteria for the equilibrium of the periodic system to those for that of quasi-periodic system,applying the method of main integration.Concretely,we showed the stability for the equilibrium x=x′=0of the quasi-periodic second order differential equation x″＋h（t）x′＋a（t）x2n＋1＋e（t,x）=0,n≥1,where h（t）,a（t）,e（t,x）are quasi-periodic coefficients,whose frequency vectors meet the requirements proposed by Diophantine.And moreover, ｜e（t,x）｜ =O（x2n＋2）near x=x′=0.The results we obtained also imply that,under some conditions,the equilibrium of the quasi-periodic oscillator with damping changing sign can still be stable.