摘要：In this paper, we study the existence of solutions of the discrete ϕ-Laplacian equation ∇ [ ϕ ( Δ u k ) ] = λ f ( k , u k , Δ u k ) $\nabla[\phi(\Delta u_{k})]=\lambda f(k, u_{k}, \Delta u_{k})$ , k ∈ [ 2 , n − 1 ] Z $k\in[2, n-1]_{\mathbb{Z}}$ , with Dirichlet or mixed boundary conditions. Under general conditions, an explicit estimate of λ 0 $\lambda_($ is given such that the problem possesses a solution for any λ < λ 0 $ \lambda <\lambda_($ .
关键词：ϕ -Laplacian ; existence ; Schauder’s fixed point theorem ; mixed boundary value problem ; Dirichlet boundary value problem
