Homoclinic orbits for second order Hamiltonian systems with asymptotically linear terms at infinity

Homoclinic Solutions for a Second-Order Nonperiodic Asymptotically Linear Hamiltonian Systems

and Applied Analysis 3 Note that the inequality (14) holds true with constantC = √ 2 if T ≥ 1/2 (see [9]). Subsequently, we may assume this condition is fulfilled. Consider a functional I : E T → R defined by

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].

Existence and Multiplicity of Homoclinic Orbits for Second-Order Hamiltonian Systems with Superquadratic Potential

and Applied Analysis 3 Theorem 3. Assume that L satisfies (L) and (L) and W satisfies (W1), (W4), (W8) and (W9). Then problem (1) possesses a nontrivial homoclinic orbit. Remark 4. In Theorem 3, we consider the existence of homoclinic orbits for problem (1) under a class of local superquadratic conditions without the (AR) condition and any periodicity assumptions on both L and W. There are func...

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

Existence of Homoclinic Orbits for Second Order Hamiltonian Systems without (ar) Condition

The existence of homoclinic orbits is obtained for a class of the second order Hamiltonian systems ü(t)−L(t)u(t)+∇W (t,u(t)) = 0, ∀t ∈ R , by the mountain pass theorem, where W(t,x) needs not to satisfy the global (AR) condition. Mathematics subject classification (2000): 34C37, 37J45, 47J30, 58E05.