Necessary and sufficient conditions for oscillation of solutions to second-order non-linear difference equations with delay argument
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Abstract
In this paper, we established necessary and sufficient conditions for the oscillation of all solutions of second-order half-linear delay difference equation of the form
$$
\Delta\left(\varphi(\zeta)(\Delta x(\zeta))^{\xi}\right)+\mu(\zeta) x^v(\eta(\zeta))=0 ; \quad \zeta \geq \zeta_0,
$$
Under the assumption $\sum_{\zeta=\zeta_0}^{\infty} \frac{1}{\varphi^{\frac{1}{\zeta}}(\zeta)}=\infty$, we consider the cases when $\xi>v$ and $\xi<v$. Further, some illustrate examples showing applicability of the new results are included.
Keywords:
Oscillation, non-oscillation, second-order, non-linear, delay, difference equationsMathematics Subject Classification:
Mathematics- Pages: 1170-1175
- Date Published: 01-01-2021
- Vol. 9 No. 01 (2021): Malaya Journal of Matematik (MJM)
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