This review paper contains a brief summary of topics and concepts related with some open
problems of planar differential systems. Most of them are related with 16th Hilbert problem …

In this work we study polynomial differential systems in the plane and define a new type of
integrability that we call Puiseux integrability. As its name indicates, the Puiseux integrability …

We consider a system of the form x˙= Pn (x, y)+ xRm (x, y), y˙= Qn (x, y)+ yRm (x, y), where
Pn (x, y), Qn (x, y) and Rm (x, y) are homogeneous polynomials of degrees n, n and m …

The relation between limit cycles of planar differential systems and the inverse integrating
factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From …

In this paper we study some aspects of the integrability problem for polynomial vector fields
x= P (x, y), y= Q (x, y). We analyze the possible existence of first integrals of the form I (x …

The integrability problem consists of finding the class of functions a first integral of a given
planar polynomial differential system must belong to. We recall the characterization of …

We provide the necessary and sufficient conditions of Liouvillian integrability for Liénard
differential systems describing nonlinear oscillators with a polynomial damping and a …

Recently a criterion has been given for determining the weakly formal Weierstrass non-
integrability of polynomial differential systems in c2. Here we extend this criterion for …

WEIERSTRASS INTEGRABILITY IN LIÉNARD DIFFERENTIAL SYSTEMS 1. Introduction
We consider the Liénard differential equations of th Page 1 WEIERSTRASS …

In this paper, we determine conditions for planar systems of the form\begin
{eqnarray*}\begin {array}{rcl}\displaystyle\frac {dx}{dt} &= &-(xy)(x^{2}-xy+ y^{2})+ x …