Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3

Joanna Janczewska, Jakub Maksymiuk
2012 Open Mathematics  
AbstractWe consider a conservative second order Hamiltonian system $$\ddot q + \nabla V(q) = 0$$ in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ {0} = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.
doi:10.2478/s11533-012-0096-5 fatcat:jfxpkrpxyvecfnqzxl4724bxne