一类二阶微分方程的无穷周期解(英文)

Infinite Periodic Solutions to a Class of Second-Order Differential Equations

通过临界点理论和Z2不变群指标理论,证得I(x)有无穷多个临界点,再由变分原理可得方程(2)与方程(3)等价,在改变条件的情况下,得出了一在二阶泛函微分方程存在无穷多个周期解.

By critical point and Z2-group index theory, the functional l（z） posesses infinite critical points and equation （2） is equivalent to equation （3） by the variational structure. In the changed conditions, we obtain infinite periodic solutions to a class of second-order differential equations （c（t）x＇（t-x））＇＋f（t,x（t）,x（t-r）,x（t-2r））=0.