Homoclinic orbits in Hamiltonian systems
β Scribed by Robert L Devaney
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 402 KB
- Volume
- 21
- 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
We study the existence of homoclinic orbits for first order time-dependent Hamiltonian systems z Λ=JH z (z, t), where H(z, t) depends periodically on t and H z (z, t) is asymptotically linear in z as |z| Q .. We also consider an asymptotically linear SchrΓΆdinger equation in R N .
We study the existence of even homoclinic orbits for the second-order Hamiltonian system ΓΌ+V u (t, u) = 0. Let V(t, u) = -K(t, u)+W(t, u) β C 1 (RΓR n , R), where K is less quadratic and W is super quadratic in u at infinity. Since the system we considered is neither autonomous nor periodic, the (PS