Twin solutions of boundary value problems for ordinary differential equations and finite difference equations

A new twin fixed-point theorem is applied first to obtain the existence of at least two positive solutions for the right focal boundary value problem y″ + f(ity) = 0, 0 <- t <- 1, y(0) = y′(1) = 0. It is applied later to obtain the existence of at least two positive solutions for the analogous discrete right focal boundary value problem Δ2u(k) + g(u(k)) = 0, k ε {0, … ,N}, u(0) = Δu(N + 1) = 0.