Iterative oscillation tests for difference equations with several non-monotone arguments

TL;DR

This paper develops explicit iterative oscillation criteria for difference equations with multiple non-monotone, potentially unbounded deviations, providing new insights into their oscillatory behavior.

Contribution

It introduces novel explicit iterative oscillation conditions for difference equations with several non-monotone, unbounded deviations, expanding existing theoretical frameworks.

Findings

Derived explicit oscillation criteria for unbounded deviations.

Provided additional oscillation results for bounded deviations.

Included illustrative examples demonstrating the oscillation tests.

Abstract

We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit iterative form. Additional results in terms of $\liminf $ are obtained for bounded deviations. Examples illustrating the oscillation tests are presented.