Hostname: page-component-7c8c6479df-p566r Total loading time: 0 Render date: 2024-03-28T17:34:31.680Z Has data issue: false hasContentIssue false

Heteroclinic and homoclinic solutions for a singular Hamiltonian system

Published online by Cambridge University Press:  31 March 2006

MARIA JOÃO BORGES
Affiliation:
Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001 LISBOA, Portugal email: mborges@math.ist.utl.pt

Abstract

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.

Type
Papers
Copyright
2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)