Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 786404, 16 pages
http://dx.doi.org/10.1155/2012/786404
Research Article

Existence of Solution to a Second-Order Boundary Value Problem via Noncompactness Measures

Wen-Xue Zhou1,2 and Jigen Peng1

1College of Sciences, Xi'an Jiaotong University, Xi'an 710049, China
2Department of Mathematics, Lanzhou Jiaotong University, Lanzhou 730070, China

Received 26 December 2011; Revised 16 February 2012; Accepted 20 February 2012

Academic Editor: Guang Zhang

Copyright © 2012 Wen-Xue Zhou and Jigen Peng. 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 and uniqueness of the solutions to the Dirichlet boundary value problem in the Banach spaces is discussed by using the fixed point theory of condensing mapping, doing precise computation of measure of noncompactness, and calculating the spectral radius of linear operator.