On the solvability of of some partial differential inequality

TL;DR

This paper examines the applicability and limitations of the Dulac criterion, a classical method used to determine the non-existence of periodic solutions in planar differential equations.

Contribution

It investigates the conditions under which the Dulac criterion can be applied or reversed, clarifying its scope in differential inequality analysis.

Findings

Identifies specific cases where the Dulac criterion is applicable.

Highlights limitations and potential reversibility of the criterion.

Provides insights into the criterion's role in ruling out periodic solutions.

Abstract

The \pn{Dulac} criterion is a classical method to rule out the existence of periodic solutions in planar differential equations. In this paper the applicability and therefore reversibility of this criterion is under consideration.