Oscillation result for half-linear delay difference equations of second-order
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Abstract
We obtained new single-condition criteria for the oscillation of second-order half-linear delay difference equation
$$
\Delta\left(\phi(\zeta)(\Delta x(\zeta))^v\right)+\rho(\zeta) x^v(\zeta-\eta)=0 ; \quad \zeta \geq \zeta_0
$$
Even in the linear case, the sharp result is new and, to our knowledge, improves all previous results. Furthermore, our method has the advantage of being simple to prove, as it relies just on sequentially improved monotonicities of a positive solution. Examples are provided to illustrate our results.
Keywords:
Oscillation, non-oscillation, second-order, delay, half-linear, difference equationsMathematics Subject Classification:
Mathematics- Pages: 1153-1159
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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