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 present a method for constructing a Dulac function for mathematical models in population biology, in the form of systems of ordinary differential equations in the plane.

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We provide sufficient conditions on the components of a vector field, which ensure the existence of Dulac functions depending on special functions for such vector field. We also present some applications and examples in order to illustrate our results.