Existence of solutions for singular boundary value problems for higher order difference equations

Abstract

We offer sufficient conditions for the existence of solutions for the boundary value problem Δny + f(m, y, Δy, ⋯ , Δn-2y) = 0, n ≥ 2, m = 0, 1, ⋯ , T (1) Δiy(0) = 0, 0 ≤ i ≤ n - 3 αΔn-2y(0) - βΔn-1y(0) = 0 (2) γΔn-2y(T + 1) + δΔn-1y(T + 1) = 0 where α, β, γ and δ are constants satisfying αγ(T + 1) + αδ + βγ > 0, α > 0, γ > 0, β ≥ 0 and δ ≥ γ.