ON A GRONWALL-TYPE INEQUALITY ON TIME SCALES

  • Choi, Sung Kyu (Department of Mathematics Chungnam National University) ;
  • Koo, Namjip (Department of Mathematics Chungnam National University)
  • 투고 : 2009.01.05
  • 심사 : 2010.02.22
  • 발행 : 2010.03.30

초록

In this paper we extend a differential inequality presented in Theorem 2.2 [6] to a dynamic inequality on time scales.

키워드

참고문헌

  1. R. P. Agarwal, Difference Equations and Inequalities, 2nd ed., Marcel Dekker, New York, 2000.
  2. D. Bainov and P. Simeonov, Integral Inequalites and Applications, Academic Publishers, Dordrecht, 1992.
  3. R. Bellman, The stability of solutions of linear Differential equations, Duke Math. J. 10 (1943), 643-647. https://doi.org/10.1215/S0012-7094-43-01059-2
  4. E. Akin-Bohner, M. Bohner, and F. Akin, Pachpatte inequality on time scales, J. Inequal. Pure and App. Math. 6 (2005), Issue 1, Article 6, 2005, 23 pages.
  5. M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduc- tion with Applications, Birkhauer, Basel, 2001.
  6. S. K. Choi, B. Kang, and N. Koo, On inequalities of Gronwall type, J. Chungcheong Math. Soc. 20 (2007), 561-568.
  7. S. Hilger, Analysis on measure chains- a unified approach to continuous and discrete calculus, Results Math. 18 (1990), 18-56. https://doi.org/10.1007/BF03323153
  8. Jiheun Kim, Difference inequalities of Gronwall type, M. S. Thesis, Chungnam National University, 2008.
  9. V. Lakshmikantham and D. Trigiante, Theory of Difference Equations with Applications to Numerical Analysis, Academic Press, San Diego, 1988.
  10. V. Lakshmikantham, S. Leela and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, New York, 1989.
  11. D. S. Mitrinovic, J. E. Pecaric and A. M. Fink, Inequlities involving functions and their integrals and derivatives, Kluwer Academic Publishers, Dordrecht, 1991.
  12. J. A. Oguntuase, On an inequality of Gronwall, J. Inequal. Pure and App. Math. 2 (2001), Issue 1, Article 9, 6 pages.
  13. B. G. Pachpatte, On note on Gronwall-Bellman inequality, J. Math. Anal. Appl. 44 (1973), 758-762. https://doi.org/10.1016/0022-247X(73)90014-0
  14. B. G. Pachpatte, On some retarded integral inequalities and applications, J. Inequal. Pure and App. Math. 3 (2002), Issue 2, Article 18, 7 pages.
  15. B. G. Pachpatte, Inequalities for Finite Difference Equations, Volume 247 of Monographs and Textbooks in Pure and Applied Mathematics. Marcel Dekker, New York, 2002.
  16. F.-H. Wong, C.-C. Yeh, and C.-H. Hong, Gronwall inequalities on time scales, Math. Inequal. & Appl. 9 (2006), 75-86.