Existence of nontrivial solutions of a two point boundary value problem for a 2n^th order nonlinear difference equation

We will show how to use the Mountain Pass Theorem to obtain nontrivial solutions of a certain two point BVP for the 2n^th order, n ∈ ℕ (formally) self-adjoint nonlinear difference equation: No periodicity assumptions will be placed on r_i,i =0, 1,…, n or f and it will be assumed that f grows superlinearly both at the origin and at infinity. An example of our results will be given.