Consider the fourth-order boundary value problem
where is continuous, such that and satisfies a technical condition ensuring that, roughly speaking, is not necessarily linearizable at and Moreover, it is assumed that there exist a non-negative function and a non-negative constant such that and for all The authors give a sufficient condition, expressed in terms of the generalized eigenvalues of the associated BVP for the existence of at least one positive solution to the given BVP. The proof is performed by applying the global P. H. Rabinowitz bifurcation theorem [Rocky Mountain J. Math. 3, 161–202 (1973; Zbl 0255.47069)].