Comparison Criteria for First Order Polynomial Differential Equations

In this paper we use the comparison method for investigation of first order polynomial differential equations. We prove two comparison criteria for these equations. The proved criteria we use to obtain some global solvability criteria for first order polynomial differential equations. On the basis od these criteria we prove some criteria for existence of a closed solution (of closed solutions) for first order polynomial differential equations. The results obtained we compare with some known results. Based on obtained results some criteria of existence of periodic orbits or limit cycles for planar autonomous systems are proved.