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

Caldiroli Paolo | Zendy

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

Author(s) -

Caldiroli Paolo

Publication year - 1997

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.19971870103

Subject(s) - mathematics , homoclinic orbit , bounded function , hamiltonian system , degenerate energy levels , lemma (botany) , hamiltonian (control theory) , mountain pass , mountain pass theorem , order (exchange) , combinatorics , class (philosophy) , pure mathematics , mathematical analysis , discrete mathematics , physics , nonlinear system , quantum mechanics , bifurcation , ecology , mathematical optimization , poaceae , finance , artificial intelligence , computer science , economics , biology

We consider the Hamiltonian system in IR N given by\documentclass{article}\pagestyle{empty}\begin{document}$\ddot u + V'(u) = 0$\end{document}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.

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