Skip to content


  • Research Article
  • Open Access

Some Nonlinear Integral Inequalities on Time Scales

Journal of Inequalities and Applications20072007:070465

  • Received: 28 August 2007
  • Accepted: 6 November 2007
  • Published:


The purpose of this paper is to investigate some nonlinear integral inequalities on time scales. Our results unify and extend some continuous inequalities and their corresponding discrete analogues. The theoretical results are illustrated by a simple example at the end of this paper.


  • Theoretical Result
  • Integral Inequality
  • Discrete Analogue
  • Continuous Inequality
  • Nonlinear Integral Inequality


Authors’ Affiliations

Department of Mathematics, Binzhou University, Shandong, 256603, China


  1. Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results in Mathematics 1990,18(1–2):18–56.MathSciNetView ArticleMATHGoogle Scholar
  2. Agarwal R, Bohner M, Peterson A: Inequalities on time scales: a survey. Mathematical Inequalities & Applications 2001,4(4):535–557.MathSciNetView ArticleMATHGoogle Scholar
  3. Akin-Bohner E, Bohner M, Akin F: Pachpatte inequalities on time scales. Journal of Inequalities in Pure Applied Mathematics 2005,6(1, article 6):23 pages.MathSciNetGoogle Scholar
  4. Bohner M, Peterson A: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston, Mass, USA; 2001:x+358.View ArticleGoogle Scholar
  5. Bohner M, Peterson A: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, Mass, USA; 2003:xii+348.View ArticleMATHGoogle Scholar
  6. Li WN: Some new dynamic inequalities on time scales. Journal of Mathematical Analysis and Applications 2006,319(2):802–814. 10.1016/j.jmaa.2005.06.065MathSciNetView ArticleMATHGoogle Scholar
  7. Pachpatte DB: Explicit estimates on integral inequalities with time scale. Journal of Inequalities in Pure Applied Mathematics 2006,7(4, article 143):8 pages.Google Scholar
  8. Wong F-H, Yeh C-C, Hong C-H: Gronwall inequalities on time scales. Mathematical Inequalities & Applications 2006,9(1):75–86.MathSciNetView ArticleMATHGoogle Scholar
  9. Pachpatte BG: On some new inequalities related to a certain inequality arising in the theory of differential equations. Journal of Mathematical Analysis and Applications 2000,251(2):736–751. 10.1006/jmaa.2000.7044MathSciNetView ArticleMATHGoogle Scholar


© W. N. Li andW. Sheng. 2007

This article is published under license to BioMed Central Ltd. 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.