Complex centers of polynomial differential equations

Electronic Journal of Differential Equations

关键词: Polynomial differential equations;    periodic solutions;    multiplicity;    centers;    Pugh problem;    Groebner bases;   

DOI  :  

来源: DOAJ

【 摘 要 】

We present some results on the existence and nonexistence of centersfor polynomial first order ordinary differential equations withcomplex coefficients. In particular, we show that binomial differentialequations 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 therelation between complex centers and the Pugh problem.An algorithm is described to solve the Pugh problem for equationswithout complex centers. The method of proof involves phase planeanalysis of the polar equations and a local study of periodic solutions.

【 授权许可】

Unknown