The existence and the uniqueness of symmetric positive solutions for a fourth-order boundary value problem

The purpose of this paper is to investigate the existence and the uniqueness of symmetric positive solutions for a class of fourth-order boundary value problem: {y((4))(t) = f(t, y(t)), t is an element of [0, 1], y(0) = y(1) = y'(0) = y'(1) = 0. By using the fixed point index method, we establish the existence of at least one or at least two symmetric positive solutions for the above boundary value problem. Further, by using a fixed point theorem of general alpha-concave operators, we also present criteria which guarantee the existence and uniqueness of symmetric positive solutions for the above boundary value problem. (C) 2011 Elsevier Ltd. All rights reserved.