Nodal solutions for a fourth-order two-point boundary value problem

We consider boundary value problems of fourth-order differential equations of the form u +βu − αu = μh(x)f (u), 00 for all u = 0, and lim u→−∞ f (u) u = 0, lim u→+∞ f (u) u = f+∞, lim u→0 f (u) u = f0 for some f+∞,f0 ∈ (0,∞). We use bifurcation techniques to establish existence and multiplicity results of nodal solutions to the problem.  2005 Elsevier Inc. All rights reserved