Infinitely many homoclinic orbits for the second-order Hamiltonian systems with super-quadratic potentials

✍ Scribed by Jie Yang; Fubao Zhang

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 417 KB
• Volume: 10
• Category: Article
• ISSN: 1468-1218
• DOI: 10.1016/j.nonrwa.2008.01.013

✦ Synopsis

We study the existence of infinitely many homoclinic orbits for some second-order Hamiltonian systems: ü -L(t)u(t) + ∇ F(t, u(t)) = 0, ∀t ∈ R, by the variant fountain Theorem, where F(t, u) satisfies the super-quadratic condition F(t, u)/|u| 2 → ∞ as |u| → ∞ uniformly in t, and need not satisfy the global Ambrosetti-Rabinowitz condition.