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Discrete Dynamics in Nature and Society
Volume 2013, Article ID 259730, 10 pages
http://dx.doi.org/10.1155/2013/259730
Research Article

Existence and Uniqueness of Positive Solutions to Nonlinear Second Order Impulsive Differential Equations with Concave or Convex Nonlinearities

1Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi 030024, China
2School of Mathematical Sciences, Shanxi University, Taiyuan, Shanxi 030006, China

Received 29 January 2013; Accepted 15 May 2013

Academic Editor: Yanbin Sang

Copyright © 2013 Lingling Zhang and Chengbo Zhai. 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

Using a new fixed point theorem of generalized concave operators, we present in this paper criteria which guarantee the existence and uniqueness of positive solutions to nonlinear two-point boundary value problems for second-order impulsive differential equations with concave or convex nonlinearities.