# Global solvability criteria for some classes of nonlinear second order ordinary differential equations

## TL;DR

This paper develops global solvability criteria for certain nonlinear second order ODEs using Riccati equations, proving oscillation theorems and applying results to Emden-Fowler and Van der Pol equations.

## Contribution

It introduces new global solvability criteria for classes of nonlinear second order ODEs using Riccati methods, with proven oscillation theorems and applications.

## Key findings

- Established global solvability criteria for specific nonlinear second order ODEs.
- Proved two oscillation theorems relevant to these equations.
- Applied results to Emden-Fowler and Van der Pol equations.

## Abstract

The Riccati equation method is used to establish some global solvability criteria for some classes of second order nonlinear ordinary differential equations. Two oscillation theorems are proved. The results are applied to the Emden - Fowler equation and to the Van der Pol type equation.