Abstract and Applied Analysis
Volume 2012 (2012), Article ID 401923, 14 pages
http://dx.doi.org/10.1155/2012/401923
Research Article

Positive Solutions for Neumann Boundary Value Problems of Second-Order Impulsive Differential Equations in Banach Spaces

Xiaoya Liu and Yongxiang Li

Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received 8 September 2011; Revised 28 December 2011; Accepted 6 January 2012

Academic Editor: Yuriy Rogovchenko

Copyright © 2012 Xiaoya Liu and Yongxiang Li. 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

The existence of positive solutions for Neumann boundary value problem of second-order impulsive differential equations −u″(t)+Mu(t)=f(t,u(t), t∈J, t≠tk, -Δu'|t=tk=Ik(u(tk)), k=1,2,…,m, u'(0)=u'(1)=θ, in an ordered Banach space E was discussed by employing the fixed point index theory of condensing mapping, where M>0 is a constant, J=[0,1], f∈C(J×K,K), Ik∈C(K,K), k=1,2,…,m, and K is the cone of positive elements in E. Moreover, an application is given to illustrate the main result.