非强制位势下二阶非自治系统周期解的存在性

Existence of Periodic Solution about Non-autonomous Second Order System with Not Coercive Potential

对于非自治二阶系统的位势函数在非强制情形下,利用归约方法和极大极小原理,充分借助空间分解的特性,利用子空间的特征,得到了关于该问题在梯度函数次线性或线性增长情形下新的存在性结果.

By using the reduction methods and the minimax theorem,the non-autonomous second order system is studied with the potential function lacking of the coercive condi- tion.Based on the decomposition of the space and the character of the subspace, we obtain the new existence of the solution for this problem involving the gradient function with the sublinear or linear growth.