An improved product type oscillation test for partial difference equations

摘要

We present new oscillation tests for the PΔEau(m+1,n)+bu(m,n+1)−cu(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.