Global solvability, stability and oscillation criteria for systems of two first-order pseudo linear ordinary differential equations

TL;DR

This paper develops criteria for the global solvability, stability, and oscillation of two-dimensional nonlinear ODE systems using Riccati and other methods, extending previous results to broader classes.

Contribution

It introduces new criteria for analyzing two-dimensional nonlinear systems, generalizing many existing results on second order nonlinear ODEs.

Findings

Established global solvability conditions

Derived stability criteria for the systems

Provided oscillation criteria with illustrative examples

Abstract

In this paper we use the Riccati equation method with other ones to establish global solvability, stability and oscillation criteria for a class of two dimensional nonlinear systems of ordinary differential equations, which is a generalization of wide classes of second order nonlinear ordinary differential equations, studied by many authors. The applicability of some of these criteria are illustrated by examples.