Homoclinic orbits for asymptotically linear 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...

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

Existence of Homoclinic Orbits for Hamiltonian Systems with Superquadratic Potentials

and Applied Analysis 3 We make the following assumptions. A1 W t, z ∈ C1 R × R2N,R is 1-periodic in t. W t, 0 0 for all t ∈ R. There exist constants c1 > 0 and μ > 2 such that Wz t, z z ≥ c1|z| for t, z ∈ R × R2N. A2 there exist c2, r > 0 such that |Wz t, z | ≤ c2|z|μ−1 for t ∈ R and |z| ≤ r. A3 there exist c3, R ≥ r and p ≥ μ such that |Wz t, z | ≤ c3|z|p−1 for t ∈ R and |z| ≥ R. A4 there exis...

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.

Homoclinic orbits for first order Hamiltonian systems with convex potentials

In this paper new estimates on the C-norm of homoclinic orbit are shown for first order convex Hamiltonian systems possessing super-quadratic potentials. Applying these estimates, some new results on the existence of infinitely many geometrically distinct homoclinic orbits are proved, which generalize the main results in [2] and [8].