Research Article
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Year 2018, Volume: 47 Issue: 3 , 601 - 613 , 01.06.2018
https://izlik.org/JA72UY58KR

Abstract

References

  • Busenberg, S. and Cooke, K.L. Models of vertically transmitted diseases with sequential- continuous dynamics, In: Nonlinear Phenomena in Mathematical Sciences, V. Lakshmikantham (Ed.), Academic Press, 179-187, 1982.
  • Dai, L. and Singh, M.C. On oscillatory motion of spring mass systems subject to piesewise constant forces, J. Sound Vib. 173, 217-233, 1994.
  • Dai, L. and Singh, M.C. An analytical and numerical method for solving linear and nonlinear vibration problems, Int. J. Solids Struct. 34, 2709-2731, 1997.
  • Cooke, K.L. and Wiener, J. Retarded dierential equations with piecewise constant delays, J. Math. Anal. Appl. 99, 265-297, 1984.
  • Aftabizadeh, A.R. and Wiener, J. Oscillatory properties of first order linear functional differential equations, Applicable Anal. 20, 165-187, 1985.
  • Aftabizadeh, A.R., Wiener, J. and Ming Xu, J. Oscillatory and periodic solutions of delay differential equations with piecewise constant argument, Proc. of American Math. Soc. 99, 673-679, 1987.
  • Shen, J.H. and Stavroulakis, I.P. Oscillatory and nonoscillatory delay equations with piece- wise constant argument, J. Math. Anal. Appl. 248, 385-401, 2000.
  • Wiener, J. Generalized Solutions of Functional Differential Equations, World Scientic, Singapore, 1994.
  • Karakoç, F., Bereketoglu H. and Seyhan, G. Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument, Acta Appl. Math. 110, 499-510, 2010.
  • Bereketoglu, H., Seyhan G. and Ogun, A. Advanced impulsive differential equations with piecewise constant arguments, Math. Model. Anal. 15, 175-187, 2010.
  • Karakoç, F., Ogun Unal, A. and Bereketoglu, H. Oscillation of nonlinear impulsive differential equations with piecewise constant arguments, E. J. Qualitative Theory of Di. Equ. No. 49, 1-12, 2013.
  • Gyori, I. and Ladas, G. Oscillation Theory of Delay Differential Equations, Oxford University Press, 1991.
  • Akhmet, M. Nonlinear Hybrid Continuous/Discrete-Time Models, Atlantis Press, Springer, 2011.
  • Gopalsamy, K., Gyori I. and Ladas, G. Oscillations of a class of delay equations with continuous and piecewise constant arguments, Funkcialaj Ekvacioj, 32, 395-406, 1989.
  • Agarwal, R.P., Karakoç, F. and Zafer, A. A survey on oscillation of impulsive ordinary differential equations, Advances in Difference Equations, Volume 2010, Article ID 354841, 52 pages, doi:10.1155/2010/354841.
  • Yan J. and Kou, C. Oscillation of solutions of impulsive delay differential equations, J. Math. Anal. Appl. 254, 358-370, 2001.
  • Agarwal, R.P. and Karakoç, F. A survey on oscillation of impulsive delay differential equa- tions, Comput. Math. Appl. 60, 1648-1685, 2010.
  • Chiu, K.S. and Pinto, M. Periodic solutions of differential equations with a general piecewise constant argument and applications, E. J. Qualitative Theory of Di. Equ., No. 46, 1-19, 2010.
  • Chiu, K.S. and Jeng, J.C. Stability of oscillatory solutions of differential equations with general piecewise constant arguments of mixed type, Mathematische Nachrichten 288(10), 1085-1097, 2015.

Oscillation of a first order linear impulsive delay differential equation with continuous and piecewise constant arguments

Year 2018, Volume: 47 Issue: 3 , 601 - 613 , 01.06.2018
https://izlik.org/JA72UY58KR

Abstract

A class of first order linear impulsive delay differential equation with continuous and piecewise constant arguments is studied. Using a connection between impulsive delay differential equations and non-impulsive delay differential equations sufficient conditions for the oscillation of the solutions are obtained.

References

  • Busenberg, S. and Cooke, K.L. Models of vertically transmitted diseases with sequential- continuous dynamics, In: Nonlinear Phenomena in Mathematical Sciences, V. Lakshmikantham (Ed.), Academic Press, 179-187, 1982.
  • Dai, L. and Singh, M.C. On oscillatory motion of spring mass systems subject to piesewise constant forces, J. Sound Vib. 173, 217-233, 1994.
  • Dai, L. and Singh, M.C. An analytical and numerical method for solving linear and nonlinear vibration problems, Int. J. Solids Struct. 34, 2709-2731, 1997.
  • Cooke, K.L. and Wiener, J. Retarded dierential equations with piecewise constant delays, J. Math. Anal. Appl. 99, 265-297, 1984.
  • Aftabizadeh, A.R. and Wiener, J. Oscillatory properties of first order linear functional differential equations, Applicable Anal. 20, 165-187, 1985.
  • Aftabizadeh, A.R., Wiener, J. and Ming Xu, J. Oscillatory and periodic solutions of delay differential equations with piecewise constant argument, Proc. of American Math. Soc. 99, 673-679, 1987.
  • Shen, J.H. and Stavroulakis, I.P. Oscillatory and nonoscillatory delay equations with piece- wise constant argument, J. Math. Anal. Appl. 248, 385-401, 2000.
  • Wiener, J. Generalized Solutions of Functional Differential Equations, World Scientic, Singapore, 1994.
  • Karakoç, F., Bereketoglu H. and Seyhan, G. Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument, Acta Appl. Math. 110, 499-510, 2010.
  • Bereketoglu, H., Seyhan G. and Ogun, A. Advanced impulsive differential equations with piecewise constant arguments, Math. Model. Anal. 15, 175-187, 2010.
  • Karakoç, F., Ogun Unal, A. and Bereketoglu, H. Oscillation of nonlinear impulsive differential equations with piecewise constant arguments, E. J. Qualitative Theory of Di. Equ. No. 49, 1-12, 2013.
  • Gyori, I. and Ladas, G. Oscillation Theory of Delay Differential Equations, Oxford University Press, 1991.
  • Akhmet, M. Nonlinear Hybrid Continuous/Discrete-Time Models, Atlantis Press, Springer, 2011.
  • Gopalsamy, K., Gyori I. and Ladas, G. Oscillations of a class of delay equations with continuous and piecewise constant arguments, Funkcialaj Ekvacioj, 32, 395-406, 1989.
  • Agarwal, R.P., Karakoç, F. and Zafer, A. A survey on oscillation of impulsive ordinary differential equations, Advances in Difference Equations, Volume 2010, Article ID 354841, 52 pages, doi:10.1155/2010/354841.
  • Yan J. and Kou, C. Oscillation of solutions of impulsive delay differential equations, J. Math. Anal. Appl. 254, 358-370, 2001.
  • Agarwal, R.P. and Karakoç, F. A survey on oscillation of impulsive delay differential equa- tions, Comput. Math. Appl. 60, 1648-1685, 2010.
  • Chiu, K.S. and Pinto, M. Periodic solutions of differential equations with a general piecewise constant argument and applications, E. J. Qualitative Theory of Di. Equ., No. 46, 1-19, 2010.
  • Chiu, K.S. and Jeng, J.C. Stability of oscillatory solutions of differential equations with general piecewise constant arguments of mixed type, Mathematische Nachrichten 288(10), 1085-1097, 2015.
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Fatma Karakoç

Publication Date June 1, 2018
IZ https://izlik.org/JA72UY58KR
Published in Issue Year 2018 Volume: 47 Issue: 3

Cite

APA Karakoç, F. (2018). Oscillation of a first order linear impulsive delay differential equation with continuous and piecewise constant arguments. Hacettepe Journal of Mathematics and Statistics, 47(3), 601-613. https://izlik.org/JA72UY58KR
AMA 1.Karakoç F. Oscillation of a first order linear impulsive delay differential equation with continuous and piecewise constant arguments. Hacettepe Journal of Mathematics and Statistics. 2018;47(3):601-613. https://izlik.org/JA72UY58KR
Chicago Karakoç, Fatma. 2018. “Oscillation of a First Order Linear Impulsive Delay Differential Equation With Continuous and Piecewise Constant Arguments”. Hacettepe Journal of Mathematics and Statistics 47 (3): 601-13. https://izlik.org/JA72UY58KR.
EndNote Karakoç F (June 1, 2018) Oscillation of a first order linear impulsive delay differential equation with continuous and piecewise constant arguments. Hacettepe Journal of Mathematics and Statistics 47 3 601–613.
IEEE [1]F. Karakoç, “Oscillation of a first order linear impulsive delay differential equation with continuous and piecewise constant arguments”, Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, pp. 601–613, June 2018, [Online]. Available: https://izlik.org/JA72UY58KR
ISNAD Karakoç, Fatma. “Oscillation of a First Order Linear Impulsive Delay Differential Equation With Continuous and Piecewise Constant Arguments”. Hacettepe Journal of Mathematics and Statistics 47/3 (June 1, 2018): 601-613. https://izlik.org/JA72UY58KR.
JAMA 1.Karakoç F. Oscillation of a first order linear impulsive delay differential equation with continuous and piecewise constant arguments. Hacettepe Journal of Mathematics and Statistics. 2018;47:601–613.
MLA Karakoç, Fatma. “Oscillation of a First Order Linear Impulsive Delay Differential Equation With Continuous and Piecewise Constant Arguments”. Hacettepe Journal of Mathematics and Statistics, vol. 47, no. 3, June 2018, pp. 601-13, https://izlik.org/JA72UY58KR.
Vancouver 1.Fatma Karakoç. Oscillation of a first order linear impulsive delay differential equation with continuous and piecewise constant arguments. Hacettepe Journal of Mathematics and Statistics [Internet]. 2018 Jun. 1;47(3):601-13. Available from: https://izlik.org/JA72UY58KR