非齐次二阶奇异Hamiltonian系

Nonhomogeneous second order singular hamiltonian systems

本文研究具有固定Ｔ周期的奇异哈密尔顿系统ｘ＋Ｖ（Ｘ）＝ｆ（ｔ）（ＨＳ）其中Ω是１ＲＮ中的开子集，Ｖ∈Ｃ１（Ω，Ｒ）且在边界有奇性，即，ｌｉｍＶ（ｘ）＝－∞，ｆ∈Ｃ（Ｒ，ＲＮ）是Ｔ周期的．应用临界点理论，我们得到结果：当Ｎ≥２且Ｖ满足强力条件时，（ＨＳ）有无穷多个Ｔ周期解；当Ｎ＝２且Ｖ不满足强力条件时，（ＨＳ）有无穷多个广义Ｔ周期解．

n this paper,we study the existence of the periodic solutions,with a fixed period T,of the singular Hamiltonian systemWhere Ω is an open subset of R, V∈C1 (Ω,R) With singularity at . i. e. lim V(x)=-∞,f∈C(R,RN) is T-periodic. By critical point theoty, the following results are obtained.When N >2 and V satisfies (SF)condition there are infinite many T-periodic solutions;when N = 2 and V doesn't satisfies (SF) condition,there are infinitely many generalized T-periodio solutions.