We study the existence of unbounded solutions of singular Hamiltonian systems: q̈ + ∇V(q)=0, (*) where V(q) ∼ -1/|q|α is a potential with a singularity. For a class of singular potentials with a strong force α > 2, we show the existence of at least one hyperbolic-like solutions. More precisely, for given H > 0 and θ+, θ- ε SN-1, we find a solution q(t) of (*) satisfying 1/2 |q̇|2 + V(q) = H, |q(t) |→ as t → ±∞ limt→±∞ q(t)/|q(t)|=θ±.
ASJC Scopus subject areas
- Applied Mathematics