Abstract

Consider the planar differential equation $x\prime =y,\; y\prime =\; h$₀(x)+h₁(x)y+ h₂(x)y²+h₃(x)y³. We prove that if a linear ordinary differential associated to it has a positive solution then we can obtain an upper bound for its number of limit cycles. The main ingredient of the proof is the Bendixson-Dulac Criterion for $m$-connected sets. Some concrete examples are also developed.

This is a joint work with H. Giacomini.