Dulac-Cherkas criterion for exact estimation of the number of limit cycles of autonomous systems on a plane (Q2358655)

The classical Dulac function extension of the Bendixson criterion for bounding the number of limit cycles that can exist in the phase portrait of a smooth system of ordinary differential equations in a region of the plane was extended by L.~A.~Cherkas using what are now widely known as Cherkas-Dulac functions. Further work by Cherkas and others led to methods of obtaining upper bounds on the number of limit cycles in a domain \(\Omega\) that contains a unique rest point. This paper constitutes a further extension involving a two-step sequence of the use of Cherkas-Dulac functions and solution of a linear programming problem in order to obtain an exact count of the number of limit cycles in \(\Omega\).