Asymptotic behaviour of solutions of higher order difference and partial difference equations with distributed deviating arguments

摘要

We shall study the asymptotic behaviour of solutions of the difference equation ∣m[y(j)+g(j)y(j−σ)]∣α−1Δm[y(j)y(j−σ)]+∑bξ=aT(j,ξ)f(y(h(j,ξ)))=0,j⩾j0 where α > 0. As an application of the results obtained, oscillation theorems are established for the partial difference equation ∣m[y(j)+g(j)y(j−σ)]+∑bξ=aʌ(i,j,ξ)f(y(h(j,ξ)))=d(j)Ly(i,j)+∑μl=1dl(j)Ly(i,tl(j)), i ϵ Ω, j