一类超线性Hill型对称碰撞方程的周期运动

The periodic motions of a class of symmetric superlinear Hill's impact equations

本文考虑一类超线性Hill型对称碰撞方程的对称碰撞周期解的存在性、重性和分布问题.通过坐标变换的方法把碰撞相平面转化为全平面进行研究,在一类关于时间映射的超线性条件下证明有外力方程无穷多个对称碰撞调和解和对称碰撞次调和解的存在性;同时研究在没有外力时方程的对称碰撞周期解的稠密性分布.本文还给出对称碰撞方程对称碰撞周期解存在的充分条件.

We are concerned with the existence, multiplicity and distribution of the even and periodic solutions of a class of symmetric superlinear Hill＇s equations with impact. We transform the impact phase-plane into a whole phase-plane by a coordinate transformation and, we prove the existence of infinite numbers of symmetric harmonic and subharmonic solutions of forced impactors as well as the densely distribution of symmetric subharmonic solutions of the unforced equations under some superlinear assumption about time-mapping. We also develop a lemma on sufficient condition for symmetric periodic solutions to symmetric second order equations.