Recent Advances in Nonlinear Partial Differential Equations: A Celebration of Norman Dancer’s 60th Birthday University of New England (Armidale), Australia, 16-21 July 2006 |
|||

## Marek IzydorekGdansk University of Technology (Poland)## Generalized heteroclinic solutions for a class of the second order Hamiltonian systemsWe shall be concerned with the existence of heteroclinic orbits for the second order Hamiltonian system
where q R - #M ≥ 2 and ,
- there exists 0 < ɛ
_{0}≤ G such that for every 0 < ɛ ≤ ɛ_{0}there is δ > 0 such that for all (t,x) R×R^{n}if d(x,M) ≥ ɛ then -V (t,x) > δ, - for every x R
^{n}\ M, , - for every x M, , where
Our result states that each point of M is joined with a certain other element of M by a solution of (HS). Since
we should not expect that (HS) possesses a stationary solution the notion of a heteroclinic orbit is
used in a generalized sense. Namely, q: R → R |