Results on the Behavior of the Solutions for Linear Impulsive Neutral Delay Differential Equations with Constant Coefficients

Year 2021, Volume: 4 Issue: 4, 180 - 189, 27.12.2021

Ali Fuat Yeniçerioğlu

https://doi.org/10.33434/cams.947259

Abstract

We have given some results regarding the behavior of solutions for first order linear impulsive neutral delay
differential equations with constant coefficients. These results were obtained using two different real roots of the
corresponding characteristic equation. Finally, two examples are given for solutions of impulsive neutral delay
differential equations.

Keywords

Neutral delay differential equation, Characteristic equation, Behavior of solutions.

References

• [1] A.F. Yenic¸erio˘glu, Stability of linear impulsive neutral delay differential equations with constant coefficients, J. Math. Anal. Appl., 479 (2019), 2196–2213.
• [2] D.D. Bainov, V. Covachev and I.M. Stamova, Estimates of the solutions of impulsive quasilinear functional differential equations, Annales de la Facultb des Sciences de Toulouse, 2 (1991), 149-161.
• [3] D.D. Bainov, V. Covachev and I.M. Stamova, Stability under persistent disturbances of impulsive differential- difference equations of neutral type, J. Math. Anal. Appl., 187 (1994), 790-808.
• [4] D.D. Bainov, I.M. Stamova, Uniform asymptotic stability of impulsive differential-difference equations of neutral type by Lyapunov’s direct method, J. Comput. and Appl. Math., 62 (1995), 359-369.
• [5] M. B. Dimitrova and V. I. Donev, Existence and asymptotic behavior of positive solutions of neutral impulsive differential equations, Nonlinear Oscillations, 8(3) (2005), 302-317.
• [6] I.M. Stamova and T.G. Stamov, Asymptotic stability of impulsive control neutral-type systems, Inter. J. of Control, 87(1) (2014), 25-31.
• [7] I.G.E. Kordonis, N.T. Niyianni and Ch.G. Philos, On the behavior of the solutions of scalar first order linear autonomous neutral delay differential equations, Arch. Math., (Basel) 71 (1998), 454-464.
• [8] Ch. G. Philos and I. K. Purnaras, On the behavior of the solutions for certain first order linear autonomous functional differential equations, Rocky Mountain J. Math., 36 (2006), 1999-2019.
• [9] R.P. Agarwal and F. Karakoc¸, A survey on oscillation of impulsive delay differential equations, Comput. and Math. with Appl., 60 (2010), 1648-1685.
• [10] G.H. Ballinger, Qualitative Theory of impulsive delay differential Equations, National Library of Canada, 1999.
• [11] X. Liu and J. Shen, Asymptotic Behavior of Solutions of Impulsive Neutral Differential Equations, Appl. Math. Letters, 12 (1999), 51-58.
• [12] X. Liu and Y.M. Zeng, Linear multistep methods for impulsive delay differential equations, Appl. Math. and Comput., 321 (2018), 555-563.
• [13] F. Jiang and J. Shen,Asymptotic behavior of solutions for a nonlinear differential equation with constant impulsive jumps, Acta Math. Hungar., 138(1–2) (2013), 1–14.
• [14] I.M. Stamova, Stability analysis of impulsive functional differential equations, Walter de Gruyter, Berlin, 2009.
• [15] Z. You and J. Wang, Stability of impulsive delay differential equations, J. Appl. Math. Comput., 56 (2018), 253-268.
• [16] G.L. Zhang, M.H. Song and M.Z. Liu, Exponential stability of the exact solutions and the numerical solutions for a class of linear impulsive delay differential equa