Positive solution of second-order multi-point boundary value problems for finite difference equation with a \(p\)-Laplacian (Q949248)

The paper is concerned with the boundary value problems for the following second-order difference equation with \(p\)-Laplacian: \[ \Delta(\varphi_p(\Delta u(k)))+\lambda q(k)f(k,u(k))=0, \] subject to multi-point boundary value conditions. The approach is to use a fixed point theorem on the cone due to Krasnosel'skii. At least one positive solution is shown to exist.