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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 912874, 6 pages
http://dx.doi.org/10.1155/2013/912874
Research Article

Some New Nonlinear Weakly Singular Inequalities and Applications to Volterra-Type Difference Equation

1School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China
2Department of Mathematics, University of Tennessee, Knoxville, TN 37996-0612, USA
3School of Business, Sichuan University, Chengdu, Sichuan 610064, China

Received 3 August 2013; Revised 21 September 2013; Accepted 25 September 2013

Academic Editor: Josef Diblík

Copyright © 2013 Kelong Zheng 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.

Abstract

Some new nonlinear weakly singular difference inequalities are discussed, which generalize some known weakly singular inequalities and can be used in the analysis of nonlinear Volterra-type difference equations with weakly singular kernel. An application to the upper bound of solutions of a nonlinear difference equation is also presented.