MULTIPLE HOMOCLINIC SOLUTIONS FOR A CLASS OF AUTONOMOUS SINGULAR SYSTEMS IN R-2

Authors
CALDIROLI P NOLASCO M
Citation
P. Caldiroli et M. Nolasco, MULTIPLE HOMOCLINIC SOLUTIONS FOR A CLASS OF AUTONOMOUS SINGULAR SYSTEMS IN R-2, Annales de l Institut Henri Poincare. Analyse non lineaire, 15(1), 1998, pp. 113-125
Citations number
18
Categorie Soggetti
Mathematics,Mathematics
Journal title
Annales de l Institut Henri Poincare. Analyse non lineaire → ACNP
ISSN journal
02941449
Volume
15
Issue
1
Year of publication
1998
Pages
113 - 125
Database
ISI
SICI code
0294-1449(1998)15:1<113:MHSFAC>2.0.ZU;2-0
Abstract
We look for homoclinic solutions for a class of second order autonomou s 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 singulariti es, namely V(x) --> -infinity as dist(x,S) --> 0. We prove that if V s atisfies 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. (C) Elsevier, Paris.