The upper and lower solution method for some fourth-order boundary value problems

In this paper, we are concerned with the fourth-order two-point boundary value problem u((iv))(t) = f(t, u(t), u'(t), u"(t), u'''(t)), 0 < t < 1, u(0) = u'(1) = u"(0) = u'''(1) = 0. By placing certain restrictions on the nonlinear term f, we obtain the existence results for the fourth-order two-point boundary value problem via the lower and upper solution method. In particular, a new truncating technique and an appropriate Nagumo-type condition are introduced and employed. (c) 2006 Elsevier Ltd. All rights reserved.