Heteroclinic and homoclinic solutions for a singular Hamiltonian system

We consider an autonomous Hamiltonian system $\ddot {q}+V_q(q)=0$ in ${\bf R}^2$, where the potential $V$ has a global maximum at the origin and singularities at some points $\xi_1$, $\xi_2 \in {\bf R}^2 \setminus \{0\}$. Under some compactness conditions on $V$ at infinity and assuming a strong for...

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Bibliographic Details
Published in:European journal of applied mathematics 2006-02, Vol.17 (1), p.1-32
Main Author: BORGES, MARIA JOÃO
Format: Article
Language:English
Subjects:
Applied mathematics
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Summary:We consider an autonomous Hamiltonian system $\ddot {q}+V_q(q)=0$ in ${\bf R}^2$, where the potential $V$ has a global maximum at the origin and singularities at some points $\xi_1$, $\xi_2 \in {\bf R}^2 \setminus \{0\}$. Under some compactness conditions on $V$ at infinity and assuming a strong force type condition at the singularities, we study, using variational arguments, the existence of various types of heteroclinic and homoclinic solutions of the system.
ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792506006516