Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/11743
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dc.contributor.authorDE MAESSCHALCK, Peter-
dc.contributor.authorDUMORTIER, Freddy-
dc.date.accessioned2011-03-03T08:42:54Z-
dc.date.availableNO_RESTRICTION-
dc.date.available2011-03-03T08:42:54Z-
dc.date.issued2011-
dc.identifier.citationJOURNAL OF DIFFERENTIAL EQUATIONS, 250(4). p. 2162-2176-
dc.identifier.issn0022-0396-
dc.identifier.urihttp://hdl.handle.net/1942/11743-
dc.description.abstractBased on geometric singular perturbation theory we prove the existence of classical Lienard equations of degree 6 having 4 limit cycles. It implies the existence of classical Lienard equations of degree n >= 6, having at least [n-1/2] + 2 limit cycles. This contradicts the conjecture from Lins, de Melo and Pugh formulated in 1976, where an upperbound of [n-1/2] limit cycles was predicted. This paper improves the counterexample from Dumortier, Panazzolo and Roussarie (2007) by supplying one additional limit cycle from degree 7 on, and by finding a counterexample of degree 6. We also give a precise system of degree 6 for which we provide strong numerical evidence that it has at least 3 limit cycles. (c) 2010 Elsevier Inc. All rights reserved.-
dc.language.isoen-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.rightsElsevier Science-
dc.subject.otherSlow–fast system; Singular perturbations; Limit cycles; Relaxation oscillation; Classical Liénard equations-
dc.subject.otherSlow-fast system; Singular perturbations; Limit cycles; Relaxation oscillation; Classical Lienard equations-
dc.titleClassical Lienard equations of degree n >= 6 can have [n-1/2]+2 limit cycles-
dc.typeJournal Contribution-
dc.identifier.epage2176-
dc.identifier.issue4-
dc.identifier.spage2162-
dc.identifier.volume250-
local.format.pages15-
local.bibliographicCitation.jcatA1-
dc.description.notes[De Maesschalck, P.; Dumortier, F.] Hasselt Univ, B-3590 Diepenbeek, Belgium.-
local.type.refereedRefereed-
local.type.specifiedArticle-
dc.bibliographicCitation.oldjcatA1-
dc.identifier.doi10.1016/j.jde.2010.12.003-
dc.identifier.isi000286447000014-
item.fulltextWith Fulltext-
item.accessRightsOpen Access-
item.contributorDE MAESSCHALCK, Peter-
item.contributorDUMORTIER, Freddy-
item.fullcitationDE MAESSCHALCK, Peter & DUMORTIER, Freddy (2011) Classical Lienard equations of degree n >= 6 can have [n-1/2]+2 limit cycles. In: JOURNAL OF DIFFERENTIAL EQUATIONS, 250(4). p. 2162-2176.-
item.validationecoom 2012-
crisitem.journal.issn0022-0396-
crisitem.journal.eissn1090-2732-
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