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Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument

Gizem S. Oztepe; Fatma Karakoc; Huseyin Bereketoglu

Communications in Mathematics (2017)

  • Volume: 25, Issue: 2, page 89-98
  • ISSN: 1804-1388

Abstract

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This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.

How to cite

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Oztepe, Gizem S., Karakoc, Fatma, and Bereketoglu, Huseyin. "Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument." Communications in Mathematics 25.2 (2017): 89-98. <http://eudml.org/doc/294391>.

@article{Oztepe2017,
abstract = {This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.},
author = {Oztepe, Gizem S., Karakoc, Fatma, Bereketoglu, Huseyin},
journal = {Communications in Mathematics},
keywords = {Oscillation; periodicity; piecewise continuous argument; impulsive differential equations},
language = {eng},
number = {2},
pages = {89-98},
publisher = {University of Ostrava},
title = {Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument},
url = {http://eudml.org/doc/294391},
volume = {25},
year = {2017},
}

TY - JOUR
AU - Oztepe, Gizem S.
AU - Karakoc, Fatma
AU - Bereketoglu, Huseyin
TI - Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument
JO - Communications in Mathematics
PY - 2017
PB - University of Ostrava
VL - 25
IS - 2
SP - 89
EP - 98
AB - This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.
LA - eng
KW - Oscillation; periodicity; piecewise continuous argument; impulsive differential equations
UR - http://eudml.org/doc/294391
ER -

References

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  1. Akhmet, M., Nonlinear hybrid continuous/discrete-time models., 2011, Springer Science & Business Media. (2011) Zbl1328.93001MR2883822
  2. Bereketoglu, H., Oztepe, G.S., 10.18514/MMN.2013.595, Miskolc Math. Notes, 14, 2013, 801-815, (2013) Zbl1299.34247MR3153966DOI10.18514/MMN.2013.595
  3. Bereketoglu, H., Oztepe, G.S., Asymptotic constancy for impulsive differential equations with piecewise constant argument, Bull. Math. Soc. Sci. Math. Roumanie Tome, 57, 2014, 181-192, (2014) MR3236647
  4. Bereketoglu, H., Seyhan, G., Ogun, A., 10.3846/1392-6292.2010.15.175-187, Math. Model. Anal, 15, 2, 2010, 175-187, (2010) Zbl1218.34095MR2604207DOI10.3846/1392-6292.2010.15.175-187
  5. Bereketoglu, H., Seyhan, G., Karakoc, F., On a second order differential equation with piecewise constant mixed arguments, Carpath. J. Math, 27, 1, 2011, 1-12, (2011) Zbl1265.34272MR2848121
  6. Busenberg, S., Cooke, K., Vertically Transmitted Diseases, Models and Dynamics, Biomathematics, 23, 1993, Springer, Berlin, (1993) Zbl0837.92021MR1206227
  7. Chen, C.H., Li, H.X., Almost automorphy for bounded solutions to second-order neutral differential equations with piecewise constant arguments, Elect. J. Diff. Eq., 140, 2013, 1-16, (2013) Zbl1292.34076MR3084620
  8. Gouzé, J.L., Sari, T., 10.1080/1468936021000041681, Dynamic. Syst., 17, 4, 2002, 299-316, (2002) Zbl1054.34013MR1975116DOI10.1080/1468936021000041681
  9. Karakoc, F., Bereketoglu, H., Seyhan, G., 10.1007/s10440-009-9458-9, Acta Appl. Math., 110, 1, 2010, 499-510, (2010) Zbl1196.34104MR2601669DOI10.1007/s10440-009-9458-9
  10. Küpper, T., Yuan, R., 10.1006/jmaa.2001.7761, J. Math. Anal. Appl., 267, 1, 2002, 173-193, (2002) Zbl1008.34063MR1886823DOI10.1006/jmaa.2001.7761
  11. Li, J., Shen, J., Periodic boundary value problems of impulsive differential equations with piecewise constant argument, J. Nat. Sci. Hunan Norm. Univ., 25, 2002, 5-9, (2002) Zbl1047.34076MR1939990
  12. Li, H.X., 10.1016/j.jmaa.2004.05.034, J. Math. Anal. Appl., 298, 2, 2004, 693-709, (2004) Zbl1064.34056MR2086984DOI10.1016/j.jmaa.2004.05.034
  13. Nieto, J.J., Lopez, R.R., 10.1016/j.jmaa.2004.09.023, J. Math. Anal. Appl., 304, 1, 2005, 33-57, (2005) Zbl1078.34046MR2124647DOI10.1016/j.jmaa.2004.09.023
  14. Oztepe, G.S., Bereketoglu, H., Convergence in an impulsive advanced differential equations with piecewise constant argument, Bull. Math. Anal. Appl., 4, 2012, 57-70, (2012) Zbl1314.34150MR2989710
  15. Seifert, G., Second order scalar functional differential equations with piecewise constant arguments, J. Difference Equ. Appl., 8, 5, 2002, 427-445, (2002) Zbl1010.34069MR1897067
  16. Wang, G.Q., Cheng, S.S., Existence of periodic solutions for second order Rayleigh equations with piecewise constant argument, Turkish J. Math., 30, 1, 2006, 57-74, (2006) Zbl1103.34064MR2215507
  17. Wiener, J., Generalized solutions of functional differential equations, 1993, Singapore, World Scientific, (1993) Zbl0874.34054
  18. Wiener, J., Lakshmikantham, V., 10.1016/S0362-546X(98)00245-4, Nonlinear Anal., 38, 1, 1999, 1-11, (1999) Zbl0945.34048MR1692949DOI10.1016/S0362-546X(98)00245-4
  19. Wiener, J., Lakshmikantham, V., Differential equations with piecewise constant argument and impulsive equations, Nonlinear Studies, 7, 1, 2000, 60-69, (2000) Zbl0997.34076MR1856579
  20. Yuan, R., 10.1016/S0362-546X(98)00316-2, Nonlinear Anal., 41, 7, 2000, 871-890, (2000) Zbl1024.34068MR1764025DOI10.1016/S0362-546X(98)00316-2

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