Estimate for the number of limit cycles of the equation dy/dx=Q(x,y)/P(x,y), where Q(x,y) and P(x,y) are polynomials

Abstract

The article gives the estimate for the number of limit cycles of the equation:dy/dx=Q(x,y)/P(x,y), where Q(x,y) and P(x,y) are polynomials. In addition, it is shown that limit cycles lie on separatrix solutions, and the element of the separatrix solution is being presented by concrete series in a small neighbourhood of a singular point.