Heteroclinic connections for a class of non-autonomous systems.
Heteroclinic orbits in plane dynamical systems
We consider general second order boundary value problems on the whole line of the type , , for which we provide existence, non-existence, multiplicity results. The solutions we find can be reviewed as heteroclinic orbits in the plane dynamical system.
Heteroclinic solutions to an asymptotically autonomous second-order equation.
Heteroclinics for a class of fourth order conservative differential equations
Higher-order Melnikov functions for single-DOF mechanical oscillators: theoretical treatment and applications.
Homoclinic and period-doubling bifurcations for damped systems
Homoclinic and periodic solutions of scalar differential delay equations
Homoclinic orbits for a class of infinite dimensional 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 orbits for an almost periodically forced singular Newtonian system in ℝ³
This work uses a variational approach to establish the existence of at least two homoclinic solutions for a family of singular Newtonian systems in ℝ³ which are subjected to almost periodic forcing in time variable.
Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems
Homoclinic solutions for a class of second order non-autonomous systems.
Homoclinic solutions for linear and linearizable ordinary differential equations.
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.