Center problem for several differential equations via Cherkas' method

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