Positive solutions for nonlinear singular third order boundary value problem

In this paper, we investigate the problem of existence of positive solutions for the nonlinear third order boundary value problem: u'''(t) + lambda a(t)f(u(t)) = 0, 0 < t < 1, u(0) = u'(0) = 0, alpha u'(1) + beta u ''(1) = 0, where lambda is a positive parameter. By using Krasnoselskii's fixed-point theorem of cone, we establish various results on the existence of positive solutions of the boundary value problem. Under various assumptions on a(t) and f(u(t)), we give the intervals of the parameter lambda which yield the existence of the positive solutions. An example is also given to illustrate the main results. (c) 2007 Elsevier B.V. All rights reserved.