Kamenev type conditions for oscillation of third order linear ordinary differential equations

TL;DR

This paper develops Kamenev type conditions using Riccati equations to determine when third order linear ODEs have oscillatory solutions, extending previous oscillation criteria.

Contribution

It introduces three new oscillation theorems that generalize Lazer's criterion for third order linear differential equations using Riccati methods.

Findings

Established three new oscillation theorems

Generalized Lazer's oscillation criterion

Provided conditions for oscillatory solutions

Abstract

The Riccati equation method is used to establish Kamenev type conditions for the existence of oscillatory solutions to third order linear ordinary differential equations. Three oscillatory theorems are proved, which generalize the Lazer's oscillation criterion.