Forced oscillation of delay difference equations via nonprincipal solution

In this paper, we obtain a new oscillation result for delay difference equations of the form Δ ( r n Δ x n ) + a nxτ n= b n ; n ∈ N under the assumption that corresponding homogenous equation Δ ( r n Δ z n ) + a n z n + 1 = 0 ; n ∈ N is nonoscillatory, where τ n ≤ n +1. It is observed that the oscillation behaviormay be altered due to presence of the delay. Extensions to forced Emden‐Fowler–type delay difference equations Δ ( r n Δ x n ) + a n | xτ n| α − 1xτ n= b n ; n ∈ N in the sublinear (0< α <1) and the superlinear (1< α ) cases are also discussed.