二阶非线性Duffing方程的周期解的存在性

The Exsistence of Periodic Solution for Second Order Nonlinear Duffing Equation

利用指数型二分性和不动点原理研究广义Duffing方程x”+g(x)=h(t,x)周期解,只需要求g(x)在局部区域内为负,且h(t, x)有界这样较弱限制下,得到方程的周期解存在性的判别法．定理推广了已知结果,同时可利用该方法研究其它系统周期解的存在性．

By using exponential dichotomy and fixed point theory, we investigate the existence of periodic solution for generalized Duffing equation x^n＋g（x）=h（t,x）, where g（x）〈0 in limited region, h（t,x） is bounded. We improve some results.Thismethod can be used to discuss the existence of periodic solutions of other equations.