Double solutions of boundary value problems for 2mth-order differential equations and difference equations

A double fixed-point theorem is applied to obtain the existence of at least two positive solutions for the boundary value problem, (−1)my(2m)(t) = f(y(t)), t ε [0, 1], y(2i)(0) = y(2i+1)(1) = 0, 0 ≤ i ≤ m−1. It is later applied to obtain the existence of at least two positive solutions for the analogous discrete boundary value problem, (−1)mΔ2mu(k) = g(u(k)), k ε {0, …, N}, Δ2iu(0) = Δ2i+1u(N + 1) = 0, 0 m − 1.