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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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