European Journal of Applied Mathematics



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Heteroclinic and homoclinic solutions for a singular Hamiltonian system


MARIA JOÃO BORGES a1
a1 Departamento de Matemática, Instituto Superior Técnico, Universidade Técnica de Lisboa, 1049-001 LISBOA, Portugal email: mborges@math.ist.utl.pt

Article author query
borges mj   [Google Scholar] 
 

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.

(Published Online March 31 2006)
(Received December 14 2005)
(Revised December 31 2005)