In this work we present an alternative method to build Dulac functions that allow one to discard the existence of periodic solutions for differential equations in the plane using partial differential equations. We give some examples to illustrate applications of these results.

In this paper we study the existence of Dulac functions for planar differential systems with perturbations or under algebraic operations (addition and multiplication) on vector fields, and also, the transformation of vector fields under affine transformations. We give some applications and examples in order to illustrate the applicability of the results.

In this work, we present some new criteria on the non-existence and uniqueness of limit cycles for the Liénard equation.

In this note, we study sufficient conditions to rule out existence of periodic orbits for differential equations of any dimension. The criteria are based on a slightly different version of a classical result due to Poincaré. Examples and applications of our results are presented. Mathematis Subject Classification: 34C25, 34C05