具有跳跃项的Duffing方程的拟周期解

Quasi-Periodic Solutions for Duffing Equation with Jumping Term

本文研究了一类具有非对称项和有界扰动项的Duffing方程。当扰动项是拟周期函数时,利用典则变换和光滑拟周期扭转映射的不变曲线定理,证明了方程任意解的有界性和拟周期解的存在性。

In this paper,we study a type of Duffing equation which has asymmetric term and jumping nonlinearity.When the perturbation term is a smooth quasi-periodic function,we prove the boundedness of all solutions and the existence of quasi-periodic solutions for the equation by canonical transformations and the invariant curve theorem for smooth quasi-periodic twist mappings.