We consider a conservative second order Hamiltonian system 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.
@article{bwmeta1.element.doi-10_2478_s11533-012-0096-5,
author = {Joanna Janczewska and Jakub Maksymiuk},
title = {Homoclinic orbits for a class of singular second order Hamiltonian systems in $\mathbb{R}$3},
journal = {Open Mathematics},
volume = {10},
year = {2012},
pages = {1920-1927},
zbl = {1261.34037},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0096-5}
}
Joanna Janczewska; Jakub Maksymiuk. Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3. Open Mathematics, Tome 10 (2012) pp. 1920-1927. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-012-0096-5/
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