Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 101, pp. 1-15.

Title: Complex centers of polynomial differential equations

Author: Mohamad Ali M. Alwash (West Los Angeles College, CA, USA)

Abstract:
 We 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.


Submitted March 19, 2007. Published July 25, 2007.
Math Subject Classifications: 34C05, 34C07, 34C25, 37C10, 13P10.
Key Words: Polynomial differential equations; periodic solutions; multiplicity;
           centers; Pugh problem; Groebner bases.