Abstract: 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 Poincaré map has twist property on the boundary of a big torus. Finaly, we obtained the existences of ainfinite number of periodic solutions of impact system repeatedly using the generlized PoincaréBirkhoff twinst theorem.

Key words: superlinear, boundness solutions, timemap, PoincaéBirkhoff twist theorem