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.
NOLASCO, MARGHERITA
1998-01-01
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.File in questo prodotto:
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