On constant-sign solutions of a system of discrete equations

We consider the following system of discrete equations u_i(k) = ∑_ℓ=0^N g_i(k, ℓ)f_i(ℓ, u₁(ℓ), u₂(ℓ), ⋯, u_n(l)), k ε {0, 1, ⋯, T}, ℓ=0 1 ≤ i ≤ n where T ≥ N > 0, 1 ≤ i ≤ n. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on {0, 1, ⋯} u _i(k) = ∑_ℓ=0^∞ g_i(k, ℓ)f_i(ℓ, u₁(ℓ), u₂(ℓ), ⋯, u_n(ℓ)), k ε {0, 1, ⋯}, 1 ≤ i ≤ n ℓ=0 for which the existence of constant-sign solutions is investigated.