一类二阶非自治系统概周期解的存在唯一性

EXISTENCE AND UNIQUENESS OF ALMOST PERIODIC SOLUTION TO A CLASS OF SECOND ORDER NONAUTONOMOUS SYSTEM

该文讨论了一类二阶非自治系统x¨ +RF′(x) x· + 1LF(x) =Ae(t)在一定条件下概周期解的存在唯一性 ,并得到了仅当a1 >0 ,a2k+ 1 ≥ 0时 ,x¨ +R(∑nk =0a2k+ 1 x2k+ 1 )′x· + 1L ∑nk =0a2k+ 1 x2k+ 1 =Ae(t) (R >0 ,L>0 ,A>0 ,e(t)为一定条件下的概周期函数 )存在概周期振荡 ,推广和改进了文 [1- 3]中的结果。

In this paper,we considered the existence and uniqueness of almost periodic solution to a class of second order nonautonomous system,also gave that only if a 1>0,a 2k+1 ≥0, x¨ +R(∑nk=0a 2k+1 x 2k+1 )′ x· +1L∑nk=0a 2k+1 x 2k+1 =Ae(t),(e(t) is an almost periodic function in some conditions) exists almost periodic oscillations,the results in [1-3] are extended and improved.