Eigenvalues and discrete boundary value problems for the one-dimensional p-laplacian

In this paper, we characterize the eigenvalues and show existence of positive solutions to discrete boundary value problem (here ϕ(s)=|s|p−2s, p>1 and λ>0 is a parameter) {Δ(ϕ(Δu(i−1)))+λF(i,u(i))=0,i∈N={1,2,…,T};u(0)=u(T+1)=0.