We look for homoclinic solutions for a class of second order autonomous Hamiltonian systems in R-2 with a potential V having a strict global maximum at the origin and a finite set S subset of R-2 of singularities, namely V(x) --> -infinity as dist(x,S) --> 0. We prove that if V satisfies a suitable geometrical property then for any k epsilon N the system admits a homoclinic orbit turning k times around a singularity xi epsilon S.

Multiple homoclinic solutions for a class of autonomous singular systems in \$\bold R^2\$R2.

Abstract

We look for homoclinic solutions for a class of second order autonomous Hamiltonian systems in R-2 with a potential V having a strict global maximum at the origin and a finite set S subset of R-2 of singularities, namely V(x) --> -infinity as dist(x,S) --> 0. We prove that if V satisfies a suitable geometrical property then for any k epsilon N the system admits a homoclinic orbit turning k times around a singularity xi epsilon S.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11697/20246`
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