Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 116, pp. 1-10.

Title: The Method of upper and lower solutions for second-order 
       non-homogeneous two-point boundary-value problem

Authors: Mei Jia    (Univ. of Shanghai, China)
         Xiping Liu (Univ. of Shanghai, China)

Abstract: 
  This paper studies the existence and uniqueness of
  solutions for a type of second-order two-point boundary-value
  problem depending on the first-order derivative through a non-linear
  term. By constructing a special cone and using the upper and lower
  solutions method, we obtain the sufficient conditions of the
  existence and uniqueness of solutions, and a monotone
  iterative sequence  solving the boundary-value problem.
  An error estimate formula is also given under the condition of
  a unique solution.
 
Submitted June 7, 2007. Published August 30, 2007.
Math Subject Classifications: 34B15, 34B27.
Key Words: Upper and lower solutions; cone; monotone iterative method.