Alwash, Mohamad Ali M.2021-08-132021-08-132007-07-25Alwash, M. A. M. (2007). Complex centers of polynomial differential equations. <i>Electronic Journal of Differential Equations, 2007</i>(101), pp. 1-15.1072-6691https://hdl.handle.net/10877/14317We 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.Text15 pages1 file (.pdf)enAttribution 4.0 InternationalPolynomial differential equationsPeriodic solutionsMultiplicityCentersPugh problemGroebner basesArticle