An improved product type oscillation test for partial difference equations

We present new oscillation tests for the PΔE a u ( m + 1 , n ) + b u ( m , n + 1 ) − c u ( m , n ) + p ( m , n ) u ( m − τ , n − σ ) = 0 , m , n = 0 , 1 , ⋯ , where a, b, c ∈ (0, ∞) and τ, σ ∈ {0, 1, ⋅⋅⋅}, and {p(m, n)} ⊂ [0, ∞). Our main result improves some of the well-known results in the literature. We also present a numerical example, where all the previous results in the literature fail to deliver an answer.