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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 623726, 4 pages
http://dx.doi.org/10.1155/2014/623726
Research Article

A Note on Gronwall’s Inequality on Time Scales

College of Mathematics and Computer Science, Fuzhou University, Fuzhou 350002, China

Received 29 May 2014; Accepted 6 June 2014; Published 1 July 2014

Academic Editor: Yonghui Xia

Copyright © 2014 Xueru Lin. 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.

Linked References

  1. M. Bohner, G. Guseinov, and A. Peterson, Introduction to the Time Scales Calculus, Advances in Dynamic Equations on Time Scales, Birkhäauser, Boston, Mass, USA, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  2. M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, Mass, USA, 2001.
  3. R. P. Agarwal, M. Bohner, and D. O'Regan, “Dynamic equations on time scales: a survey,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 1–26, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. P. Agarwal, M. Bohner, and D. O'Regan, “Time scale boundary value problems on infinite intervals,” Journal of Computational and Applied Mathematics, vol. 141, no. 1-2, pp. 27–34, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. L. Erbe, A. Peterson, and P. Řeháka, “Comparison theorems for linear dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol. 275, no. 1, pp. 418–438, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  6. L. Erbe and A. Peterson, “Green functions and comparison theorems for di ff erential equations on measure chains,” Dynamics of Continuous, Discrete and Impulsive Systems, vol. 6, no. 1, pp. 121–137, 1999. View at MathSciNet · View at Scopus
  7. W. N. Li, “Some integral inequalities useful in the theory of certain partial dynamic equations on time scales,” Computers and Mathematics with Applications, vol. 61, no. 7, pp. 1754–1759, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. W. N. Li, “Some delay integral inequalities on time scales,” Computers & Mathematics with Applications, vol. 59, no. 6, pp. 1929–1936, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. Y. H. Xia, J. Cao, and M. Han, “A new analytical method for the linearization of dynamic equation on measure chains,” Journal of Differential Equations, vol. 235, no. 2, pp. 527–543, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. Y. Xia, X. Chen, and V. G. Romanovski, “On the linearization theorem of Fenner and Pinto,” Journal of Mathematical Analysis and Applications, vol. 400, no. 2, pp. 439–451, 2013. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  11. Y.-H. Xia, J. Li, and P. J. Y. Wong, “On the topological classification of dynamic equations on time scales,” Nonlinear Analysis: Real World Applications, vol. 14, no. 6, pp. 2231–2248, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Y. Xia, “Global analysis of an impulsive delayed Lotka-Volterra competition system,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1597–1616, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. Y. H. Xia, “Global asymptotic stability of an almost periodic nonlinear ecological model,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4451–4478, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. Y. Xia and M. Han, “New conditions on the existence and stability of periodic solution in Lotka-Volterra's population system,” SIAM Journal on Applied Mathematics, vol. 69, no. 6, pp. 1580–1597, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. Y. Gao, X. Yuan, Y. Xia, and P. J. Y. Wong, “Linearization of impulsive differential equations with ordinary dichotomy,” Abstract and Applied Analysis, vol. 2014, Article ID 632109, 11 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  16. Y. Gao, Y. Xia, X. Yuan, and P. Wong, “Linearization of nonautonomous impulsive system with nonuniform exponential dichotomy,” Abstract and Applied Analysis, vol. 2014, Article ID 860378, 7 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Y. Xia, X. Yuan, K. I. Kou, and P. J. Y. Wong, “Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy,” Abstract and Applied Analysis, vol. 2014, Article ID 725098, 10 pages, 2014. View at Publisher · View at Google Scholar · View at MathSciNet