Periodic solutions for singular Hamiltonian systems and closed geodesics on non-compact Riemannian manifolds
The author deals with the so-called prescribed energy problem: \[ \ddot q+ \nabla V(q)= 0, \qquad \tfrac 12 |\dot q|^2+ V(q)= H, \] where \(q(t): \mathbb{R}\to \mathbb{R}^N \setminus \{0\}\), \(N\geq 2\), \(V: \mathbb{R}^n \setminus \{0\}\to \mathbb{R}\) and \(H\in \mathbb{R}\). The author studies the existence of periodic solutions of similar Hamiltonian systems as well as the existence of closed geodesics on noncompact Riemannian manifolds in a related situation.
scientific article; zbMATH DE number 1441846