Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/8263
Title: Hilbert's 16th problem for classical Lienard equations of even degree
Authors: CAUBERGH, Magdalena 
DUMORTIER, Freddy 
Issue Date: 2008
Publisher: ACADEMIC PRESS INC ELSEVIER SCIENCE
Source: JOURNAL OF DIFFERENTIAL EQUATIONS, 244(6). p. 1359-1394
Abstract: Classical Lienard equations are two-dimensional vector fields, on the phase plane or on the Lienard plane, related to scalar differential equations <(x)double over dot> + f(x)<(x) over dot> + x = 0. In this paper, we consider f to be a polynomial of degree 2l - 1, with I a fixed but arbitrary natural number. The related Lienard equation is of degree 2l. We prove that the number of limit cycles of such an equation is uniformly bounded, if we restrict f to some compact set of polynomials of degree exactly 2l - 1. The main problem consists in studying the large amplitude limit cycles, of which we show that there are at most l. (c) 2007 Elsevier Inc. All rights reserved.
Notes: Hasselt Univ, B-3590 Diepenbeek, Belgium.Dumortier, F, Hasselt Univ, Campus Diepenbeek,Gebouw D, B-3590 Diepenbeek, Belgium.magdalena.caubergh@uhasselt.be freddy.dumortier@uhasselt.be
Keywords: classical lienard equation; limit cycle; heteroclinic connection; Cyclicity
Document URI: http://hdl.handle.net/1942/8263
ISSN: 0022-0396
e-ISSN: 1090-2732
DOI: 10.1016/j.jde.2007.11.011
ISI #: 000255005700004
Category: A1
Type: Journal Contribution
Validations: ecoom 2009
Appears in Collections:Research publications

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