Positive solutions of nonlinear singular third-order two-point boundary value problem

In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem u"'(t) + lambda a(t)f(u(t)) = 0, 0 < t < 1, U(0) = u'(0) = u"(1) = 0, where lambda is a positive parameter. Under various assumptions on a and f we establish intervals of the parameter; which yield the existence of at least one, at least two, and infinitely many positive solutions of the boundary value problem by using Krasnoselskii's fixed point theorem of cone expansion-compression type. (c) 2005 Elsevier Inc. All rights reserved.