𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Even homoclinic orbits for super quadratic Hamiltonian systems

✍ Scribed by Jian Ding; Junxiang Xu; Fubao Zhang

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
124 KB
Volume
33
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

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) ∈ C 1 (RΓ—R 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) condition is difficult to check when we use the Mountain Pass theorem. Therefore, we approximate the homoclinic orbits by virtue of the solutions of a sequence of nil-boundary-value problems.

πŸ“œ SIMILAR VOLUMES

Homoclinic Orbits for Asymptotically Lin
Homoclinic Orbits for Asymptotically Linear Hamiltonian Systems
✍ Andrzej Szulkin; Wenming Zou πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 320 KB

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 .

Multiple Homoclinics for a Class of Sing
Multiple Homoclinics for a Class of Singular Hamiltonian Systems
✍ Paolo Caldiroli; Colette De Coster πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 256 KB

## 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