Electron. J. Diff. Eqns., Vol. 2007(2007), No. 116, pp. 1-10.

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

Mei Jia, Xiping Liu

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.

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Mei Jia
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: jiamei-usst@163.com
Xiping Liu
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: xipingliu@163.com

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