Comparison criteria for first order polynomial differential equations

TL;DR

This paper develops comparison criteria for first order polynomial differential equations, enabling the derivation of global solvability and closed solution existence conditions, and compares these with existing results.

Contribution

It introduces new comparison criteria for first order polynomial differential equations and applies them to establish global solvability and closed solution existence.

Findings

Established two new comparison criteria for these equations.

Derived global solvability conditions based on the criteria.

Provided criteria for the existence of closed solutions.

Abstract

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 of these criteria we prove some criteria for existence of a closed solution (of closed solutions) of for first order polynomial differential equations. The results obtained we compare with some known results.