关于超线性Duffing方程的碰撞周期解的存在性  

The existence of bouncing periodic solutions for a superlinear Duffing equation

作　　者：马青[1] 

机构地区：[1]浙江工业大学理学院,浙江杭州310023

出　　处：《浙江工业大学学报》2010年第6期693-698,共6页Journal of Zhejiang University of Technology

摘　　要：Duffing方程在机械振动和电子工程技术中有许多重要的应用,它描述了共振现象、调和振动、次调和振动、概周期振动、拟周期振动、奇异吸引子和混沌这些现象的存在.因此,在非线性振动理论中研究Duffing方程不仅具有重要的理论意义,还具有非常重要的应用价值.主要通过后继函数的方法并利用Poincaré-Birkhoff扭转定理来研究超线性Duffing方程的碰撞周期解的存在性,证明了一类超线性Duffing方程以2mπ为周期的碰撞周期解的存在性,并给出了在每个周期内存在n个零点的充分条件.Dulling equtions have many important applications in Mechanical Vibration and Electronic Engineering Technology. They discribe the existences of resonance phenomenon, harmonic vibration, subharmonic vibration, almost periodic vibration, quasi-periodic vibration, chaos, and strange attractors. Thus, in non-linear vibration theory, research of Dulling equation is not only of an important theoretical significance, but also has a very important application value. In this paper, by using the method of successor map and the Poincare-Birkhoff twist theorem, we research the existence of boucing solutions for superlinear Duffing equations. It is proved that the boucing 2turf-periodic solutions for sufficient conditions which guarantee the existence a superlinear Dulling equation is exist and the of n impacts in one period are given.

关 键 词：超线性Duffing方程 碰撞周期解 后继函数 Poincaré-Birkhoff扭转定理 

分 类 号：O175.14[理学—数学]