中文摘要：

运用相平面定性分析方法，研究一类带不变号权函数二阶微分方程的碰撞问题．通过坐标变换将碰撞问题转化为与之等价的定义在全平面上的问题，在某种超线性条件下对解的动态行为进行分析，得到了大振幅解的动态行为．结果表明，Poincar6映射在充分大的圆环边界上具有扭转性，并通过反复运用推广的Poincare-Birkhoff扭转定理，得到了无穷多个ω-周期碰撞解的存在性．

英文摘要：

The present paper deals with a class of superlinear equations with weight. Firstly, introducing a new coordinate transformation, we translated the impact system into a new equal system, which is defined on the whole plane. Secondly, under a certain super-linear condition, we analyzed the solutions and got the dynamics of the solutions of big norms. We found that the Poincare map has twist property on the boundary of a big torus. Finaty, we obtained the existences of a infinite number of periodic solutions of impact system repeatedly using the generlized Poincare-Birkhoff twinst theorem.