Homoclinic and periodic orbits for hamiltonian systems
Homoclinic orbits for a class of singular second order Hamiltonian systems in ℝ3
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.
Homoclinic orbits for a class of symmetric Hamiltonian systems.
Homoclinic solutions for a class of second order non-autonomous systems.
Homoclinic solutions for second-order non-autonomous Hamiltonian systems without global Ambrosetti-Rabinowitz conditions.
Homoclinic solutions of 2nth-order difference equations containing both advance and retardation
By using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.
Homoclinics : Poincaré-Melnikov type results via a variational approach
Hyperbolic characteristics on star-shaped hypersurfaces