Electronic Journal of Differential Equations,
Vol. 2011 (2011), No. 21, pp. 1-7.

Title: A priori estimates for solutions to a four point boundary
       value problem for singularly perturbed semilinear 
       differential equations

Author: Robert Vrabel (Slovak Technical Univ., Trnava, Slovakia)

Abstract: 
 This article concerns the existence and asymptotic behavior
 of solutions to a singularly perturbed second-order
 four-point boundary-value problem for nonlinear differential
 equations. Our analysis relies on the method of lower and
 upper solutions. We give accurate  approximations of the
 solutions up to order $O(\epsilon)$.

Submitted January 5, 2010. Published February 07, 2011.
Math Subject Classifications: 34K10, 34K26.
Key Words: Singular perturbation; four point boundary value problem;
           lower and upper solutions.