Global Existence of Homoclinic and Periodic Orbits for a Class of Autonomous Hamiltonian Systems
β Scribed by B. Buffoni; J.F. Toland
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 645 KB
- Volume
- 118
- Category
- Article
- ISSN
- 0022-0396
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π SIMILAR VOLUMES
## Abstract We consider the Hamiltonian system in IR^__N__^ given by where __V__ : IR^__N__^ rarr; IR is a smooth potential having a non degenerate local maximum at 0 and we assume that there is an open bounded neighborhood ft of 0 such that V(__x__) < __V__(0) for __x__ Ξ΄ Ξ© / {0}, __V(x)__ = __V
## RN \_ S Βͺ R has a unique strict global maximum at a point p g R N and a singular Under some compactness conditions on V at 1 infinity and around the singular set S we study the existence of homoclinic orbits to p which link with S. When V and G satisfy suitable geometrical conditions, we can p
We consider an autonomous Hamiltonian system u +{V(u)=0 where the potential V : R 2 "[!] Γ R has a strict global maximum at the origin and a singularity at some point !{0. Under some compactness conditions on V at infinity and around the singularity ! we study the existence of homoclinic orbits to 0