Limit cycles for a variant of a generalized Riccati equation

In this paper we provide a lower bound for the maximum number of limit cycles surrounding the origin of systems (ẋ,ẏ=ẍ) given by a variant of the generalized Riccati equation ẍ+εx2n+1ẋ+bx4n+3=0,where b>0, b∈R, n is a non-negative integer and ε is a small parameter. The tool for proving this result uses Abelian integrals.