Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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IMPULSIVE INTEGRAL INEQUALITIES WITH A NON-SEPARABLE KERNEL

  • Choi, Sung Kyu (Department of Mathematics Chungnam National University) ;
  • Koo, Namjip (Department of Mathematics Chungnam National University) ;
  • Ryu, Chunmi (Department of Mathematics Chungnam National University)
  • Received : 2014.08.28
  • Accepted : 2014.09.26
  • Published : 2014.11.15
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Abstract

In this paper we present some Gronwall-tpye inequalities with a non-separable kernel and obtain the explicit estimate for solutions of impulsive differential equations. Furthermore, we give an example to illustrate our results.

Keywords

References

  1. D. D. Bainov and P. S. Simeonov, Systems with Impulsive Effect: Stability, Theory and Applications, Ellis Horwood Series in Mathematics and Its Application, 1989.
  2. D. D. Bainov and P. S. Simeonov, Impulsive Differential Equations: Asymptotic Propertites of the Solutions, World Scientific Publishing Co., Inc., River Edge, NJ, 1995.
  3. S. K. Choi, N. Koo, and C. Ryu, Stability of linear impulsive differential equations via $t_{\infty}$-similarity, Chungcheong Math. Soc. 26 (2013), 811-819. https://doi.org/10.14403/jcms.2013.26.4.811
  4. V. Lakshmikantham, D. D. Bainov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific Publishing Co. Pte. Ltd., Singapore, 1989.
  5. V. Lakshmikantham, S. Leela, and A. A. Martynyuk, Stability Analysis of Nonlinear Systems, Marcel Dekker, INC., New York and Basel, 1989.

Cited by

  1. A NOTE ON LINEAR IMPULSIVE FRACTIONAL DIFFERENTIAL EQUATIONS vol.28, pp.4, 2015, https://doi.org/10.14403/jcms.2015.28.4.583
  2. ON EXACT SOLUTIONS FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH NON-INTEGER ORDERS vol.29, pp.3, 2016, https://doi.org/10.14403/jcms.2016.29.3.515