Existence of positive solutions of a nonlinear fourth-order boundary value problem

Abstract

In this paper, we study the existence of positive solutions of fourth-order boundary value problem u(4) (t) = f (t, u (t), u″ (t)), t ∈ (0, 1),u (0) = u (1) = u″ (0) = u″ (1) = 0, where f : [0, 1] × [0, ∞) × (- ∞, 0] → [0, ∞) is continuous. The proof of our main result is based upon the Krein-Rutman theorem and the global bifurcation techniques. © 2010 Elsevier Ltd. All rights reserved.