Existence of solution for a class of nth-order multi-point boundary value problem

In this paper, we are concerned with the following nth-order ordinary differential equation x(n)(t)+f(t,x(t),x'(t),⋯,x (n-1)(t))=0, t ∈ (0,1),with the nonlinear boundary conditions x(i)(0)=0,i=0,1,⋯,n-3,g(x(n-2)}(0),x (n-1)(0),x(ξ1),⋯,x(ξm-2))=A,h(x (n-2)(1),x(n-1)(1),x(η1),⋯,x(ηl-2))=B,here A,B ∈ R, f:[0,1]×R n →R is continuous, g:[0,1]×R m →R is continuous, h:[0,1]×R l →R is continuous, ξ i (0,1), i=1,⋯,m-2, and η j (0,1), j=1,⋯,l-2. The existence result is given by using a priori estimate, Nagumo condition, the method of upper and lower solutions and Leray-Schauder degree. We also give an example to demonstrate our result. © 2009 Korean Society for Computational and Applied Mathematics.