Communications in Mathematical Analysis

Gronwall-like Inequalities On Time Scales with Applications

Elvan Akın-Bohner and Mehmet Ünal

Full-text: Open access


Some new nonlinear dynamic integral inequalities of Gronwall type for retarded functions are established. These inequalities can be used as basic tools in the study of certain classes of functional dynamic equations as well as dynamic delay equations.

Article information

Commun. Math. Anal., Volume 11, Number 2 (2011), 23-35.

First available in Project Euclid: 25 February 2011

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 39A10

measure chain time scales gronwall inequalities dynamic equations delay equations


Akın-Bohner, Elvan; Ünal, Mehmet. Gronwall-like Inequalities On Time Scales with Applications. Commun. Math. Anal. 11 (2011), no. 2, 23--35.

Export citation


  • R. Agarwal, Difference Equations and Inequalities, Marcel Dekker, New York, 1992.
  • R. Agarwal, M. Bohner and A. Peterson, Inequalities on time scales: a survey. Math. Inequal. Appl. 4 (2001), pp 535-557.
  • R. Agarwal, Y. H. Kim and S. K. Sen, New retarded discrete inequalities with applications, Int. J. Difference Equ., 4 (2009), pp 1-19.
  • R. Agarwal, Y. H. Kim and S. K. Sen, New nonlinear integral inequalities with applications, Functional Differential Equations, 16 (2009), pp 19-33.
  • E. Ak\in-Bohner, M. Bohner and F. Ak\in, Pachpatte inequalities on time scales, J. Inequal. Pure. Appl. Math., 6 (2005), Art. 6. [ONLINE:].
  • D. R. Anderson, Nonlinear Dynamic Integral Inequalities in two Independent Variables on Time Scale Pairs, Advances in Dynamical Systems and Applications, 3 (2008), pp 1-13.
  • M. Bohner and A. Peterson, Dynamic Equations on Time Scales, An Introduction with Applications, Birkhäuser, Boston, 2001.
  • M. Bohner and A. Peterson, editors, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston, 2003.
  • B.G. Pachpatte, Inequalities for Finite Difference Equations, Marcel Dekker, New York, 2002.
  • B.G. Pachpatte, On some new inequalities related to certain inequalities in the theory of differential equations, J. Math. Anal. Appl. 189 (1995), pp 128-144.
  • B.G. Pachpatte, Inequalities for Differential and Integral Equations, Academic Press, New York, 1988.
  • S. Hilger, Ein Ma$\beta $kettenkalkül mit A nwendung auf Zentrumsmannigfaltigkeiten, PhD thesis, Universität W ürzburg, 1988.
  • P. Rehak, Hardy inequality on time scales and its application to half–linear dynamic equations, J. Inequal. Appl., 5 (2005), pp 495-507.
  • F. Wong, C. C. Yeh and C. H. Hong, Gronwall inequalities on time scales, Math. Inequal. Appl., 1 (2006), pp 75-86.