BibTex RIS Kaynak Göster

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

Yıl 2017, Cilt: 66 Sayı: 2, 115 - 129, 01.08.2017
https://doi.org/10.1501/Commua1_0000000806

Öz

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

Kaynakça

  • 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
Yıl 2017, Cilt: 66 Sayı: 2, 115 - 129, 01.08.2017
https://doi.org/10.1501/Commua1_0000000806

Öz

Kaynakça

  • 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
Toplam 18 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

S.gizem Oztepe Bu kişi benim

Yayımlanma Tarihi 1 Ağustos 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 66 Sayı: 2

Kaynak Göster

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. Ağustos 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, sy. 2 (Ağustos 2017): 115-29. https://doi.org/10.1501/Commua1_0000000806.
EndNote Oztepe S (01 Ağustos 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., c. 66, sy. 2, ss. 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 (Ağustos 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, c. 66, sy. 2, 2017, ss. 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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