Multiple positive solutions of second-order nonlinear difference equations with discrete singular φ-Laplacian

Abstract

ABSTRACTWe consider the discrete boundary value problems with mean curvature operator in the Minkowski space where is a parameter, n>4 and q>1. Using upper and lower solutions, topological methods and Szulkin's critical point theory for convex, lower semicontinuous perturbations of -functionals, we show that there exists such that the above problem has zero, at least one or two positive solutions according to , or . Moreover, Λ is strictly decreasing with respect to n.