Communications in Applied Analysis 19 (2015), 487–496 TWO NONTRIVIAL SOLUTIONS FOR A DISCRETE FOURTH ORDER PERIODIC BOUNDARY VALUE PROBLEM

where N ≥ 1 is an integer, ∆ is the forward difference operator defined by ∆u(t) = u(t + 1) − u(t), ∆u(t) = u(t), ∆u(t) = ∆(∆u(t)) for i ≥ 1, p : [0, N ]Z → R with p(0) = p(N), q : [1, N ]Z → R, f : [1, N ]Z × R → R is continuous in its second argument, and λ is a positive parameter. By a solution of BVP (1.1), we mean a function u : [−1, N + 2]Z → R such that u satisfies (1.1). Difference equations appear naturally as discrete analogues and as numerical solutions of differential equations and delay differential equations which model various diverse phenomena in statistics, computing, electrical circuit analysis, dynamical systems, economics, and biology (see, for example, [1, 17, 18]). In recent years, many