We look for homoclinic solutions for a class of second order autonomous Hamiltonian systems in $\mathbb{R}^2$ with a potential $V$ having a strict global maximum at the origin and a finite set $S\subset\mathbb{R}^2$ of singularities, namely $V(x)\to-\infty$ as dist$\,(x,S)\to 0$. We prove that if $V$ satisfies a suitable geometrical property then for any $k\in\N$ the system admits a homoclinic orbit turning $k$ times around a singularity $\xi\in S$.
Multiple homoclinic solutions for a class of autonomous singular systems in R2
CALDIROLI, Paolo;
1998-01-01
Abstract
We look for homoclinic solutions for a class of second order autonomous Hamiltonian systems in $\mathbb{R}^2$ with a potential $V$ having a strict global maximum at the origin and a finite set $S\subset\mathbb{R}^2$ of singularities, namely $V(x)\to-\infty$ as dist$\,(x,S)\to 0$. We prove that if $V$ satisfies a suitable geometrical property then for any $k\in\N$ the system admits a homoclinic orbit turning $k$ times around a singularity $\xi\in S$.
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