Center Problem for Several Differential Equations via Cherkas' Method

Cherkas' method characterizes centers for analytic Liénard differential equations. We extend his method to degenerate Liénard differential equations and we apply this extension to solve the center problem for several families of polynomial differential equations. In particular, we give all centers for some differential equations given by a vector field which is the sum of two quasi-homogeneous ones. © 1998 Academic Press.