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Abstract and Applied Analysis
Volume 2014, Article ID 259016, 9 pages
Research Article

Nonlinear Sum Operator Equations with a Parameter and Application to Second-Order Three-Point BVPs

1Department of Mathematics, Taiyuan Normal University, Taiyuan 030012, China
2Department of Mathematics and Statistics, Qinghai Nationalities University, Xining 810007, China
3School of Mathematics, Jinzhong University, Jinzhong 030600, China

Received 29 November 2013; Revised 25 January 2014; Accepted 27 January 2014; Published 16 March 2014

Academic Editor: Erdal Karapınar

Copyright © 2014 Wen-Xia Wang et al. 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.


A class of nonlinear sum operator equations with a parameter on order Banach spaces were considered. The existence and uniqueness of positive solutions for this kind of operator equations and the dependence of solutions on the parameter have been obtained by using the properties of cone and nonlinear analysis methods. The critical value of the parameter was estimated. Further, the application to some nonlinear three-point boundary value problems was given to show the significance of the discussion.