一类奇异 Hamilton 系统的周期解

T PERIODIC SOLUTIONS OF A CLASS OF SINGULAR HAMILTONIAN SYSTEMS

本文研究方程Ａｘ＝Ｖ（ｘ）＋ｆ（ｔ）（ＨＳ）在无界奇点集下的周期与广义周期解存在性问题，其中ｘ＝（ｘ１，…，ｘｎ），ｘｉ∈Ｒ２（１≤ｉ≤ｎ），Ａ是Ｒ２×…×Ｒ２上的正定矩形，Ｃ∈Ｃ１，ｆ是以Ｔ为周期的可积函数。

This paper studies the existence of T-periodic solutions of the system A=V(x)+f(t)(HS) where A is a positive definitely matrix on R 2×…×R 2,and V is singular with unbounded singular sets,and proves the existence of infinitely many T-periodic and generalized T-periodic solutions.