Oscillation and non-oscillation criteria for second order linear non homogeneous functional-differential equations

TL;DR

This paper develops generalized oscillation and non-oscillation criteria for second order linear nonhomogeneous functional-differential equations using Riccati equation methods, extending Wong's criteria for ordinary differential equations.

Contribution

It introduces a new set of oscillation criteria for functional-differential equations that generalize existing results for ordinary differential equations.

Findings

The criteria effectively determine oscillation behavior.

The criteria are demonstrated through two illustrative examples.

Abstract

The Riccati equation method is used to establish oscillation and non-oscillation criteria for second order linear nonhomogeneous functional-differential equations.We show that the obtained oscillation criterion is a generalization of J. S. W. Wong's oscillation criterion for second order linear nonhomogeneous ordinary differential equations. Two examples, demonstrating the aptitude of the obtained criteria, are presented.