KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2017 / Volume: 46 Issue: 6

Existence and qualitative properties of solutions of a second order mixed type impulsive differential equation with piecewise constant arguments

Gizem S. Oztepe
Sayfa
—
Yayın Tarihi
2017-12-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Moreover, we study oscillation, non-oscillation and periodicity of the solutions.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We prove the existence and uniqueness of the solutions of a second order mixed type impulsive differential equation with piecewise constant arguments.
📊
Temel Bulgular & Veri:We prove the existence and uniqueness of the solutions of a second order mixed type impulsive differential equation with piecewise constant arguments.
💡
Sonuç & Katkı:Moreover, we study oscillation, non-oscillation and periodicity of the solutions.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Existence of solutions · Oscillation · Non-oscillation

Abstract

We prove the existence and uniqueness of the solutions of a second order mixed type impulsive differential equation with piecewise constant arguments. Moreover, we study oscillation, non-oscillation and periodicity of the solutions.

🔖

Bu Makaleye Atıf Yap

Oztepe, G. S. (2017). Existence and qualitative properties of solutions of a second order mixed type impulsive differential equation with piecewise constant arguments. Hacettepe Journal of Mathematics and Statistics, Volume: 46 Issue: 6. https://ajindex.com/articles/1402988

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (26)

  1. Huang, Y.K. Oscillations and asymptotic stability of solutions of first order neutral differential equations with piecewise constant argument, The Journal of Mathematical Analysis and Applications 149 (1), 70-85, 1990.
  2. Fu, X. and Li, X. Oscillation of higher order impulsive differential equations of mixed type with constant argument at fixed time, Mathematical and Computer Modelling 48 (5), 776- 786, 2008.
  3. Bereketoglu, H., Seyhan, G. and Ogun, A. Advanced impulsive differential equations with piecewise constant arguments, Mathematical Modelling and Analysis 15 (2), 175-187, 2010.
  4. Karakoc, F., Bereketoglu, H. and Seyhan, G. Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument, Acta Applicandae Mathematicae 110 (1), 499-510, 2010.
  5. Huang, C. Oscillation and nonoscillation for second order linear impulsive differential equations, The Journal of Mathematical Analysis and Applications 214 (2), 378-394, 1997.
  6. Berezansky, L. and Braverman, E. On oscillation of a second order impulsive linear delay differential equation, The Journal of Mathematical Analysis and Applications 233 (1), 276- 300, 1999.
  7. Peng, M. and Ge, W. Oscillation criteria for second-order nonlinear differential equations with impulses, Computers and Mathematics with Applications 39 (5), 217-225, 2000.
  8. Yan, J. Oscillation properties of a second-order impulsive delay differential equation, Computers and Mathematics with Applications 47 (2), 253-258, 2004.
  9. Luo, Z. and Shen, J. Oscillation of second order linear differential equations with impulses, Applied Mathematics Letters 20 (1), 75-81, 2007.
  10. Ozbekler, A. and Zafer, A. Nonoscillation and oscillation of second-order impulsive differential equations with periodic coefficients, Applied Mathematics Letters 25 (3), 294-300, 2012.
  11. Ozbekler, A. and Zafer, A. Forced Oscillation of second-order impulsive differential equations with mixed nonlinearities in: Differential and Difference Equations with Applications. (Springer New York, 2013), 183-195.
  12. Leung, A. Y. T. Direct method for the steady state response of structures, The Journal of Sound and Vibration 124 (1), 135-139, 1988.
  13. Dai, L. and Singh, M. C. On oscillatory motion of spring-mass systems subjected to piecewise constant forces, The Journal of Sound and Vibration 173 (2), 217-231, 1994.
  14. Dai, L. and Singh, M. C. An analytical and numerical method for solving linear and nonlinear vibration problems, The International Journal of Solids and Structures 34 (21), 2709- 2731, 1997.
  15. Dai, L. and Singh, M. C.Periodic, quasiperiodic and chaotic behavior of a driven Froude pendulum, The International Journal of Non-Linear Mechanics 33 (6), 947-965, 1998.
  16. Wiener, J. and Lakshmikantham, V.Excitability of a second-order delay differential equation, Nonlinear Analysis: Theory, Methods and Applications 38 (1), 1-11, 1999.
  17. Seifert, G. Second order scalar functional differential equations with piecewise constant arguments, Journal of Difference Equations and Applications 8 (5), 427-445, 2002.
  18. Chen, C.H. and Li, H.X. Almost automorphy for bounded solutions to second-order neutral differential equations with piecewise constant arguments, Electronic Journal of Differential Equations 2013 (140), 1-16, 2013.
  19. Li, H.X. Almost periodic solutions of second-order neutral delay–differential equations with piecewise constant arguments, The Journal of Mathematical Analysis and Applications 298 (2), 693-709, 2004.
  20. Yuan, R. Pseudo-almost periodic solutions of second-order neutral delay differential equations with piecewise constant argument Nonlinear Analysis: Theory, Methods and Applications 41 (7), 871-890, 2000.
  21. Yang, P., Liu, Y. and Ge, W. Green’s function for second order differential equations with piecewise constant arguments Nonlinear Analysis: Theory, Methods and Applications 64 (8), 1812-1830, 2006.
  22. Nieto, J.J. and Lopez, R. R. Green’s function for second-order periodic boundary value problems with piecewise constant arguments The Journal of Mathematical Analysis and Applications 304 (1), 33-57, 2005.
  23. Dads, E. A. and Lhachimi, L. New approach for the existence of pseudo almost periodic solutions for some second order differential equation with piecewise constant argument Nonlinear Analysis: Theory, Methods and Applications 64 (6), 1307-1324, 2006.
  24. Lopez, R. R. Nonlocal boundary value problems for second-order functional differential equations Nonlinear Analysis: Theory, Methods and Applications 74 (18), 7226-7239, 2011.
  25. Yuan, R. On the spectrum of almost periodic solution of second-order differential equations with piecewise constant argument Nonlinear Analysis: Theory, Methods and Applications 59 (8), 1189-1205, 2004.
  26. Bereketoglu, H., Seyhan, G. and Karakoc, F. On a second order differential equation with piecewise constant mixed arguments Carpathian Journal of Mathematics 27 (1), 1-12, 2011.