New potential condition on homoclinic orbits for a class of discrete Hamiltonian systems

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

Homoclinic orbits for discrete Hamiltonian systems with subquadratic potential

where n ∈ Z, u ∈ RN , u(n) = u(n + ) – u(n) is the forward difference operator, p,L : Z→ RN×N and W : Z× RN → R. As usual, we say that a solution u(n) of system (.) is homoclinic (to ) if u(n)→  as n→±∞. In addition, if u(n) ≡ , then u(n) is called a nontrivial homoclinic solution. In general, system (.) may be regarded as a discrete analogue of the following second order Hamiltonian sy...

Subharmonic solutions and homoclinic orbits of second order discrete Hamiltonian systems with potential changing sign

On Homoclinic and Heteroclinic Orbits for Hamiltonian Systems

We extend some earlier results on existence of homoclinic solutions for a class of Hamiltonian systems. We also study heteroclinic solutions. We use variational approach.

Singular Perturbation Theory for Homoclinic Orbits in a Class of Near-Integrable Hamiltonian Systems∗

This paper describes a new type of orbits homoclinic to resonance bands in a class of near-integrable Hamiltonian systems. It presents a constructive method for establishing whether small conservative perturbations of a family of heteroclinic orbits that connect pairs of points on a circle of equilibria will yield transverse homoclinic connections between periodic orbits in the resonance band r...