Existence of solutions for a class of third-order nonlinear boundary value problems

In this paper, we are concerned with the following third-order ordinary differential equation: x (t )+ f t,x(t),x (t ), x (t ) = 0, 0 < t <1, with the nonlinear boundary conditions x(0) = 0, g x (0), x (0) = A, h x (1), x (1) = B, where A,B ∈ R, f : [0, 1] × R3 →R is continuous, g,h : R2 →R are continuous. The existence result is given by using a priori estimate, Nagumo condition, upper and lower solutions and Leray– Schauder degree, and we give an example to demonstrate our result.  2004 Elsevier Inc. All rights reserved.