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TitleComplex centers of polynomial differential equations.
Author(s) M. Kalinin
TypeArticle in Journal
AbstractWe present some results on the existence and nonexistence of centers for polynomial first order ordinary differential equations with complex coefficients. In particular, we show that binomial differential equations without linear terms do not have complex centers. Classes of polynomial differential equations, with more than two terms, are presented that do not have complex centers. We also study the relation between complex centers and the Pugh problem. An algorithm is described to solve the Pugh problem for equations without complex centers. The method of proof involves phase plane analysis of the polar equations and a local study of periodic solutions.
URL http://www.emis.de/journals/EJDE/Volumes/2007/101/abstr.html
JournalElectron. J. Differ. Equ.
PublisherSouthwest Texas State University, Department of Mathematics, San Marcos, TX; North Texas State Unive
Translation No
Refereed No