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Opial inequalities on time scales

Martin BohnerBıllûr Kaymakçalan — 2001

Annales Polonici Mathematici

We present a version of Opial's inequality for time scales and point out some of its applications to so-called dynamic equations. Such dynamic equations contain both differential equations and difference equations as special cases. Various extensions of our inequality are offered as well.

Oscillation of third-order delay difference equations with negative damping term

Martin BohnerSrinivasan GeethaSrinivasan SelvarangamEthiraju Thandapani — 2018

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

The aim of this paper is to investigate the oscillatory and asymptotic behavior of solutions of a third-order delay difference equation. By using comparison theorems, we deduce oscillation of the difference equation from its relation to certain associated first-order delay difference equations or inequalities. Examples are given to illustrate the main results.

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