{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T14:11:22Z","timestamp":1772287882148,"version":"3.50.1"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"11","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,11]]},"abstract":"<jats:p>We prove that some 2\u03c0-periodic generalized Abel equations of the form x\u2032 = A(t)x<jats:sup>n<\/jats:sup>+ B(t)x<jats:sup>m<\/jats:sup>+ C(t)x, with n \u2260 m and n, m \u2265 2 have at most three limit cycles. The novelty of our result is that, in contrast with other results of the literature, our hypotheses allow the functions A,B, and C to change sign. Finally we study in more detail the Abel equation x\u2032 = A(t)x<jats:sup>3<\/jats:sup>+ B(t)x<jats:sup>2<\/jats:sup>, where the functions A and B are trigonometric polynomials of degree one.<\/jats:p>","DOI":"10.1142\/s0218127409025195","type":"journal-article","created":{"date-parts":[[2010,2,24]],"date-time":"2010-02-24T01:07:55Z","timestamp":1266973675000},"page":"3869-3876","source":"Crossref","is-referenced-by-count":27,"title":["LIMIT CYCLES FOR SOME ABEL EQUATIONS HAVING COEFFICIENTS WITHOUT FIXED SIGNS"],"prefix":"10.1142","volume":"19","author":[{"given":"J. L.","family":"BRAVO","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Extremadura, 06071 Badajoz, Spain"}]},{"given":"M.","family":"FERN\u00c1NDEZ","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Universidad de Extremadura, 06071 Badajoz, Spain"}]},{"given":"A.","family":"GASULL","sequence":"additional","affiliation":[{"name":"Departament de Matem\u00e0tiques, Edifici C, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Spain"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2006.11.004"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.12.016"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2009.06.031"},{"key":"rf4","doi-asserted-by":"crossref","first-page":"1493","DOI":"10.3934\/cpaa.2009.8.1493","volume":"8","author":"\u00c1lvarez A.","journal-title":"Commun. Pure Appl. Anal."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500021971"},{"key":"rf6","series-title":"Israel Program for Scientific Translations","volume-title":"Qualitative Theory of Second-Order Dynamic Systems","author":"Andronov A. A.","year":"1973"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2007.12.060"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1017\/S0308210500026755"},{"key":"rf9","first-page":"666","volume":"5","author":"Cherkas L. A.","journal-title":"Diff. Eq."},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1006\/jdeq.1998.3420"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1137\/0521068"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2004.07.030"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406017130"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/BF01390315"},{"key":"rf15","first-page":"277","volume":"20","author":"Lloyd N. G.","journal-title":"J. London Math. Soc."},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/BF02316287"},{"key":"rf17","volume-title":"Non-Local Problems of the Theory of Oscillations","author":"Pliss V. A.","year":"1966"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127409025195","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,28]],"date-time":"2020-05-28T14:25:49Z","timestamp":1590675949000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127409025195"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,11]]},"references-count":17,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,11]]}},"alternative-id":["10.1142\/S0218127409025195"],"URL":"https:\/\/doi.org\/10.1142\/s0218127409025195","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,11]]}}}