A New Proof of the Existence of Homoclinic Orbits for a Class of Autonomous Second Order Hamiltonian Systems in IR.N

✍ Scribed by Paolo Caldiroli

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 356 KB
• Volume: 187
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19971870103

✦ Synopsis

Abstract

We consider the Hamiltonian system in IR^N^ given by
where V : IR^N^ rarr; IR is a smooth potential having a non degenerate local maximum at 0 and we assume that there is an open bounded neighborhood ft of 0 such that V(x) < V(0) for x δ Ω / {0}, V(x) = V(0) and V′(x) ≠ 0 for x ∈ ∂Ω. Using a refined version of the mountain pass lemma [4], we give a further proof of the existence of a solution of ü + V′(u) = 0, homoclinic to 0.