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CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT

Year 2017, Volume: 66 Issue: 2, 115 - 129, 01.08.2017
https://doi.org/10.1501/Commua1_0000000806

Abstract

We prove the existence and uniqueness of the solutions of an impulsive diğerential system with a piecewise constant argument. Moreover, we obtain sufficient conditions for the convergence of these solutions and then prove that the limits of the solutions can be calculated by a formula

References

  • F. V. Atkinson and J. R. Haddock, Criteria for asymptotic constancy of solutions of functional diğerential equations, J. Math. Anal. Appl., 91 (1983), 410-423.
  • J. Bastinec, J. Diblik, and Z. Smarda, Convergence tests for one scalar diğerential equation with vanishing delay, Arch. Math. (Brno), 36 (2000), 405-414.
  • H. Bereketoglu and A. Huseynov, Convergence of solutions of nonhomogeneous linear diğer- ence systems with delays, Acta Appl. Math., 110(1) (2010), 259-269.
  • H. Bereketoglu and F. Karakoc, Asymptotic constancy for impulsive delay diğerential equa- tions, Dynam. Systems Appl., 17(1) (2008), 71-83.
  • H. Bereketoglu and F. Karakoc, Asymptotic constancy for a system of impulsive pantograph equations, Acta Math. Hungar., 145 (2015), 1-12.
  • H. Bereketoglu, M. E. Kavgaci and G. S. Oztepe, Asymptotic convergence of solutions of a scalar q-diğerence equation with double delays, Acta Math. Hungar. 148(2) (2016), 279-293.
  • H. Bereketoglu and G. S. Oztepe, Convergence of the solution of an impulsive diğerential equation with piecewise constant arguments, Miskolc Math. Notes, 14(3) (2013), 801-815.
  • H. Bereketoglu and G. S. Oztepe, Asymptotic constancy for impulsive diğerential equations with piecewise constant argument, Bull. Math. Soc. Sci. Math., 57(2) (2014), 181-192.
  • H. Bereketoglu and M. Pituk, Asymptotic constancy for nonhomogeneous linear diğerential equations with unbounded delays, Dynamical Systems and Diğerential Equations (Wilming- ton, NC, 2002). Discrete Contin. Dyn. Syst., (2003), 100-107.
  • L. Berezansky, J. Diblik, M. Ruzickova and Z. Suta, Asymptotic convergence of the solutions of a discrete equation with two delays in the critical case, Abstr. Appl. Anal., (2011), 15pp.
  • J. Diblik, A criterion of asymptotic convergence for a class of nonlinear diğerential equations with delay, Nonlinear Anal., 47(6) (2001), 4095-4106.
  • J. Diblik and M. Ruzickova, Convergence of the solutions of the equationy (t)= _y (t)= (t) [y (t ) y (t )]in the critical case, J. Math. Anal. Appl.,331(2) (2007), 1361-1370.
  • I. Györi, F. Karakoc and H. Bereketoglu, Convergence of solutions of a linear impulsive diğerential equations system with many delays, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 18(2) (2011), 191-202.
  • L. S. Hahn and B. Epstein. Classical complex analysis. Royal Society of Chemistry, (1996).
  • F. Karakoc and H. Bereketoglu, Some results for linear impulsive delay diğerential equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 16 (3) (2009), 313-326.
  • G. S. Oztepe and H. Bereketoglu, Convergence in an impulsive advanced diğerential equations with piecewise constant argument, Bull. Math. Anal. Appl., 4 (2012), 57-70.
  • A. M. Samoilenko and N. A. Perestyuk, Impulsive Diğerential Equations. World Scienti…c, (1995).
  • Current address : Gizem. Mathematics, Ankara, TURKEY S. OZTEPE :Ankara University, Faculty of Sciences, Dept. of E-mail address : gseyhan@ankara.edu.tr
Year 2017, Volume: 66 Issue: 2, 115 - 129, 01.08.2017
https://doi.org/10.1501/Commua1_0000000806

Abstract

References

  • F. V. Atkinson and J. R. Haddock, Criteria for asymptotic constancy of solutions of functional diğerential equations, J. Math. Anal. Appl., 91 (1983), 410-423.
  • J. Bastinec, J. Diblik, and Z. Smarda, Convergence tests for one scalar diğerential equation with vanishing delay, Arch. Math. (Brno), 36 (2000), 405-414.
  • H. Bereketoglu and A. Huseynov, Convergence of solutions of nonhomogeneous linear diğer- ence systems with delays, Acta Appl. Math., 110(1) (2010), 259-269.
  • H. Bereketoglu and F. Karakoc, Asymptotic constancy for impulsive delay diğerential equa- tions, Dynam. Systems Appl., 17(1) (2008), 71-83.
  • H. Bereketoglu and F. Karakoc, Asymptotic constancy for a system of impulsive pantograph equations, Acta Math. Hungar., 145 (2015), 1-12.
  • H. Bereketoglu, M. E. Kavgaci and G. S. Oztepe, Asymptotic convergence of solutions of a scalar q-diğerence equation with double delays, Acta Math. Hungar. 148(2) (2016), 279-293.
  • H. Bereketoglu and G. S. Oztepe, Convergence of the solution of an impulsive diğerential equation with piecewise constant arguments, Miskolc Math. Notes, 14(3) (2013), 801-815.
  • H. Bereketoglu and G. S. Oztepe, Asymptotic constancy for impulsive diğerential equations with piecewise constant argument, Bull. Math. Soc. Sci. Math., 57(2) (2014), 181-192.
  • H. Bereketoglu and M. Pituk, Asymptotic constancy for nonhomogeneous linear diğerential equations with unbounded delays, Dynamical Systems and Diğerential Equations (Wilming- ton, NC, 2002). Discrete Contin. Dyn. Syst., (2003), 100-107.
  • L. Berezansky, J. Diblik, M. Ruzickova and Z. Suta, Asymptotic convergence of the solutions of a discrete equation with two delays in the critical case, Abstr. Appl. Anal., (2011), 15pp.
  • J. Diblik, A criterion of asymptotic convergence for a class of nonlinear diğerential equations with delay, Nonlinear Anal., 47(6) (2001), 4095-4106.
  • J. Diblik and M. Ruzickova, Convergence of the solutions of the equationy (t)= _y (t)= (t) [y (t ) y (t )]in the critical case, J. Math. Anal. Appl.,331(2) (2007), 1361-1370.
  • I. Györi, F. Karakoc and H. Bereketoglu, Convergence of solutions of a linear impulsive diğerential equations system with many delays, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 18(2) (2011), 191-202.
  • L. S. Hahn and B. Epstein. Classical complex analysis. Royal Society of Chemistry, (1996).
  • F. Karakoc and H. Bereketoglu, Some results for linear impulsive delay diğerential equations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 16 (3) (2009), 313-326.
  • G. S. Oztepe and H. Bereketoglu, Convergence in an impulsive advanced diğerential equations with piecewise constant argument, Bull. Math. Anal. Appl., 4 (2012), 57-70.
  • A. M. Samoilenko and N. A. Perestyuk, Impulsive Diğerential Equations. World Scienti…c, (1995).
  • Current address : Gizem. Mathematics, Ankara, TURKEY S. OZTEPE :Ankara University, Faculty of Sciences, Dept. of E-mail address : gseyhan@ankara.edu.tr
There are 18 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

S.gizem Oztepe This is me

Publication Date August 1, 2017
Published in Issue Year 2017 Volume: 66 Issue: 2

Cite

APA Oztepe, S. (2017). CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 66(2), 115-129. https://doi.org/10.1501/Commua1_0000000806
AMA Oztepe S. CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2017;66(2):115-129. doi:10.1501/Commua1_0000000806
Chicago Oztepe, S.gizem. “CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66, no. 2 (August 2017): 115-29. https://doi.org/10.1501/Commua1_0000000806.
EndNote Oztepe S (August 1, 2017) CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66 2 115–129.
IEEE S. Oztepe, “CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 66, no. 2, pp. 115–129, 2017, doi: 10.1501/Commua1_0000000806.
ISNAD Oztepe, S.gizem. “CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 66/2 (August 2017), 115-129. https://doi.org/10.1501/Commua1_0000000806.
JAMA Oztepe S. CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66:115–129.
MLA Oztepe, S.gizem. “CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 66, no. 2, 2017, pp. 115-29, doi:10.1501/Commua1_0000000806.
Vancouver Oztepe S. CONVERGENCE OF SOLUTIONS OF AN IMPULSIVE DIFFERENTIAL SYSTEM WITH A PIECEWISE CONSTANT ARGUMENT. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2017;66(2):115-29.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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