In this paper, we obtain some new criteria for the oscillation of certain third-order difference equations using comparison principles with a suitable couple of first-order difference equations. The presented results improve and extend the earlier ones. Examples are provided to illustrate the main results.

This paper deals with the oscillation of a certain class of second order difference equations with a sub-linear neutral term. Using some inequalities and Riccati type transformation, four new oscillation criteria are obtained. Examples are included to illustrate the main results.

This paper deals with the oscillation of solutions of certain class of neutral difference equation ∆(an∆(χn + pnχαn−k)) + qnχβn+1−l = 0, where α and β are ratio of odd positive integers. New sufficient conditions are obtained for the oscillation of studied equation and examples illustrating the main results are provided.

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