Sign-changing solutions on a kind of fourth-order Neumann boundary value problem ✩

In this paper, we consider the fourth-order Neumann boundary value problem u(4)(t) − 2u (t) + u(t) = f (t,u(t)) for all t ∈ [0, 1] and subject to u (0) = u (1) = u (0) = u (1) = 0. Using the fixed point index and the critical group, we establish the existence theorem of solutions that guarantees the problem has at least one positive solution and two sign-changing solutions under certain conditions. © 2008 Elsevier Inc. All rights reserved