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
We shall be concerned with the existence of heteroclinic orbits for the second order Hamiltonian system
where q Rn and V C1(R ×Rn,R), V ≤ 0. We will assume that V and a certain subset M ⊂ Rn satisfy the following conditions:
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 → Rn is a generalized heteroclinic solution of (HS) if there exist x,y Rn, x≠y such that q joins x to y, (i.e. limt→-∞q(t) = x, limt→+∞q(t) = y).