Journal of Applied Mathematics and Stochastic Analysis
Volume 14 (2001), Issue 2, Pages 183-187
doi:10.1155/S1048953301000132

A monotone iterative method for boundary value problems of parametric differential equations

Xinzhi Liu1 and Farzana A. McRae2

1University of Waterloo, Department of Applied Mathematics, Waterloo N2L 3G1, Ontario, Canada
2Catholic University of America, Department of Mathematics, Washington 20057, DC, USA

Received 1 June 1997; Revised 1 June 2000

Copyright © 2001 Xinzhi Liu and Farzana A. McRae. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper studies boundary value problems for parametric differential equations. By using the method of upper and lower solutions, monotone sequences are constructed and proved to converge to the extremal solutions of the boundary value problem.