本文利用变分方法给出了具不对称非线性项的二阶常微分方程周期解的存在性的充分条件,通过例子说明本文的主要结果可看作是Landesman-Lazer条件的补充。

By means of a variational approach, we provide sufficient conditions for the existence of periodic solutions for scalar second order differential equations with asymmetric nonlinearities. Main result of this paper is illustrated with examples and can be seen as a supplement to the Landesman-Lazer condition.