# Qualitative Behavior of the Solutions to Delay and Difference Euations

## DOI:

https://doi.org/10.26577/jmmcs-2018-2-494## Keywords:

oscillation, delay differential equations, difference equations## Abstract

It is noteworthy to observe that a first-order linear ordinary differential equation without delay

does not possess oscillatory solutions. Therefore the investigation of oscillatory solutions is of

interest for equations with delays or for the discrete analogue difference equations. Furthermore, the

mathematical modelling of several real-world problems leads to differential equations that depend

on the past history rather than only the current state. In this article conditions are presented

such that all solutions of delay and difference equations are oscillatory while all solutions of the

corresponding ordinary differential equations without delay are, for example, decreasing and tend

to zero. Equations with constant and variable arguments are investigated. Several examples of

delay and difference equations with applications to many sectors of life are presented.

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*Journal of Mathematics, Mechanics and Computer Science*,

*98*(2), 3–11. https://doi.org/10.26577/jmmcs-2018-2-494