{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T22:50:30Z","timestamp":1772837430841,"version":"3.50.1"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2014,5]]},"abstract":"<jats:p> We consider the class of polynomial differential equations \u1e8b = \u03bbx + P<jats:sub>n<\/jats:sub>(x, y), \u1e8f = \u03bcy + Q<jats:sub>n<\/jats:sub>(x, y) in \u211d<jats:sup>2<\/jats:sup> where P<jats:sub>n<\/jats:sub>(x, y) and Q<jats:sub>n<\/jats:sub>(x, y) are homogeneous polynomials of degree n &gt; 1 and \u03bb \u2260 \u03bc, i.e. the class of polynomial differential systems with a linear node with different eigenvalues and homogeneous nonlinearities. For this class of polynomial differential equations, we study the existence and nonexistence of limit cycles surrounding the node localized at the origin of coordinates. <\/jats:p>","DOI":"10.1142\/s0218127414500655","type":"journal-article","created":{"date-parts":[[2014,5,28]],"date-time":"2014-05-28T08:08:41Z","timestamp":1401264521000},"page":"1450065","source":"Crossref","is-referenced-by-count":9,"title":["On the Limit Cycles of the Polynomial Differential Systems with a Linear Node and Homogeneous Nonlinearities"],"prefix":"10.1142","volume":"24","author":[{"given":"Jaume","family":"Llibre","sequence":"first","affiliation":[{"name":"Departament de Matem\u00e0tiques, Universitat Aut\u00f2noma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain"}]},{"given":"Jiang","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"}]},{"given":"Xiang","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, and MOE-LSC, Shanghai Jiao Tong University, Shanghai 200240, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2014,5,28]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2013.01.032"},{"key":"rf2","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1017\/S0308210500026755","volume":"109","author":"Carbonell M.","journal-title":"Proc. Roy. Soc. Edinburgh"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(89)90021-8"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(86)90055-0"},{"key":"rf5","series-title":"Universitext","volume-title":"Qualitative Theory of Planar Differential Systems","author":"Dumortier F.","year":"2006"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(87)90140-9"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0396(87)90185-9"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0396(03)00199-2"},{"key":"rf10","series-title":"Translations of Math. Monographs","doi-asserted-by":"crossref","DOI":"10.1090\/mmono\/094","volume-title":"Finiteness Theorems for Limit Cycles","volume":"94","author":"Ilyashenko Yu.","year":"1991"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127403006352"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1017\/S0013091500021179"},{"key":"rf13","first-page":"302","volume":"193","author":"Li C.","journal-title":"Ann. Diff. Eqs."},{"key":"rf14","first-page":"2192","volume":"46","author":"Llibre J.","journal-title":"J. Diff. Eqs."},{"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\/978-94-009-4632-3_25"},{"key":"rf17","volume-title":"Li\u00e7oes de Equa\u00e7oes Diferenciais Ordin\u00e1rias, Euclid project","volume":"11","author":"Sotomayor J.","year":"1979"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218127414500655","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:23:25Z","timestamp":1565123005000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127414500655"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,5]]},"references-count":16,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2014,5,28]]},"published-print":{"date-parts":[[2014,5]]}},"alternative-id":["10.1142\/S0218127414500655"],"URL":"https:\/\/doi.org\/10.1142\/s0218127414500655","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,5]]}}}