摘要
证明了以下的Ｎ体型问题无穷多个非碰撞Ｔ周期解的存在性：－¨ｕｉ＝Ｖ’ｕｉ（ｕ，ｔ）．其中ｕ＝（ｕ１，…，ｕＮ），ｕｉ∈Ｒｋ且Ｖ（ｕ，ｔ）＝∑１≤ｉ≠ｊ≤ＮＶｉｊ（ｕｉ－ｕｊ，ｔ），势函数Ｖｉｊ（ξ）对ｔ是Ｔ周期且在ξ＝０奇异但满足Ｇｏｒｄｏｎ的强力条件。证明基于Ｋ．Ｕｈｌｅｎｂｅｃｋ，丁伟岳及Ｐ．ＭａｊｅｒＳ．Ｔｅｒａｃｉｎｉ的扰动方法的一个变形。
We prove the existence of infinitely many non collision T periodic solutions for N body type problems: - i=V u i (u,t). Where u=(u 1,…,u N),u i∈ R k and V(u,t)=∑1≤i≠j≤NV ij (u i-u j,t) ,the potentials V ij (ξ) are T periodic in t and singular at ξ=0 which satisfy the strong force condition of Gordon. The proofs are based on a variant of the perturbation methods of K.Uhlenbeck,W.Ding,P.Majer and S.Terracini.
出处
《重庆大学学报（自然科学版）》
EI
CAS
CSCD
1998年第6期133-138,共6页
Journal of Chongqing University
关键词
N-体型问题
非碰撞周期解
无穷多周期解
周期解
N body type problems
infinitely many non collision periodic solutions
Ljusternik Schnirelmann theory
