Existence of positive solutions for difference systems coming from a model for burglary

In this paper, we use the Brouwer degree to prove existence results of positive solutions for the following difference systems: Dk∆ (Ak−1 −Ak−1)− (Ak −Ak) +Nkf(k,Ak) = 0, k ∈ [2, n− 1]Z, ∆Nk−1 +∆[g(k,Ak,∆Ak−1)Nk]− w(Nk − 1) = 0, k ∈ [2, n− 1]Z, ∆A1 = 0 = ∆An−1, ∆N1 = 0 = ∆Nn−1, where the assumptions on w, Dk, A 0 k, f , and g are motivated by some mathematical models for the burglary of houses.