Homoclinic orbits for a class of Hamiltonian systems
Homoclinic orbits for a class of Hamiltonian systems
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DOI：
10.1017/s0308210500024240
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
P. Rabinowitz
中科院分区：
文献类型：
--
作者：
P. Rabinowitz
考虑二阶Hamilton系统：其中q n，V）在t中是T周期的。假设Vq（t，0）= 0，0是V（t，.）和V（t，x）|X| → ∞在这些和一些附加的技术假设下，我们证明了（HS）有一个从0发出的同宿轨道q。当k → ∞时，得到了（HS）的2kT周期解（即次谐波）qk的极限轨道q.次谐波qk又通过山路定理得到。
Synopsis Consider the second order Hamiltonian system: where q ∊ ℝn and V ∊ C1 (ℝ ×ℝn ℝ) is T periodic in t. Suppose Vq (t, 0) = 0, 0 is a local maximum for V(t,.) and V(t, x) | x| → ∞ Under these and some additional technical assumptions we prove that (HS) has a homoclinic orbit q emanating from 0. The orbit q is obtained as the limit as k → ∞ of 2kT periodic solutions (i.e. subharmonics) qk of (HS). The subharmonics qk are obtained in turn via the Mountain Pass Theorem.