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Homoclinic orbits for a class of Hamiltonian systems
Published online by Cambridge University Press: 14 November 2011
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.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 1-2 , 1990 , pp. 33 - 38
- Copyright
- Copyright © Royal Society of Edinburgh 1990
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