Existence and multiplicity of positive solutions for discrete anisotropic equations

In this paper we consider the Dirichlet problem for a discrete anisotropic equation with some function α , a nonlinear term f , and a numerical parameter λ : ∆ (α (k) |∆u(k − 1)|^p(k−1)−2 ∆u(k − 1)) + λf (k, u(k)) = 0, k ∈ [1, T ] . We derive the intervals of a numerical parameter λ for which the considered BVP has at least 1, exactly 1, or at least 2 positive solutions. Some useful discrete inequalities are also derived.