Some New Oscillation Criteria for Fourth-Order Nonlinear Delay Difference Equations

Abstract

In this paper, the authors studied oscillatory behavior of solutions of fourth-order delay difference equation $\Delta \left(c_3\left(n\right)\Delta \left(c_2\left(n\right)\Delta \left(c_1\left(n\right)\Delta u\left(n\right)\right)\right)\right)+p\left(n\right)f\left(u\left(n-k\right)\right)=0$ under the conditions . New oscillation criteria have been obtained which greatly reduce the number of conditions required for the studied equation. Some examples are presented to show the strength and applicability of the main results.