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Heteroclinic orbits in plane dynamical systems

Luisa Malaguti, Cristina Marcelli (2002)

Archivum Mathematicum

We consider general second order boundary value problems on the whole line of the type u ' ' = h ( t , u , u ' ) , u ( - ) = 0 , u ( + ) = 1 , for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the ( u , u ' ) plane dynamical system.

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

Joanna Janczewska, Jakub Maksymiuk (2012)

Open Mathematics

We consider a conservative second order Hamiltonian system q ¨ + 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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