Abstract
We 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.
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Janczewska, J., Maksymiuk, J. Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3 . centr.eur.j.math. 10, 1920–1927 (2012). https://doi.org/10.2478/s11533-012-0096-5
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DOI: https://doi.org/10.2478/s11533-012-0096-5