Homoclinic orbits at infinity for second order conservative systems (Q1346267)

The author studies Hamiltonian systems of the second order, that is systems of the form \(\ddot q(t) + V'(q(t)) = 0\), where \(q(t) \in \mathbb{R}^ N\), \(N \geq 2\), and the potential \(V \in C^ 2 (\mathbb{R}^ N; \mathbb{R})\) has an improper maximum at infinity. The main result in the paper gives sufficient conditions for the existence of at least one homoclinic orbit at infinity, under decay conditions on the potential as \(| x | \to + \infty\).