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Oscillation Criteria for First Order Neutral Impulsive Difference Equations with Constant Coefficients

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Abstract

In this work, we have discussed the oscillation properties of first order neutral impulsive difference equations with constant coefficients by using pulsatile constant. Also, we have made an effort to apply our constant coefficient results to nonlinear impulsive difference equations with variable coefficients.

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References

  1. Gyori, I., Ladas, G.: Oscillation Theory of Delay Differential Equations with Applications. Claredon Press, New York (1991)

    MATH  Google Scholar 

  2. Lakshmikantham, V., Bainov, D.D., Simieonov, P.S.: Oscillation Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)

    Book  Google Scholar 

  3. Li, J., Shen, J.: Positive solutions for first order difference equations with impulses. Int. J. Differ. Equ. 10, 225–239 (2006)

    MATH  Google Scholar 

  4. Li, X., Xi, Q.: Oscillatory and asymptotic properties of impulsive difference equations with time-varying delays. Int. J. Differ. Equ. 4, 201–209 (2009)

    Google Scholar 

  5. Li, Q.L., Zhang, Z.G., Gou, Z.G., Liang, Z.G.: Oscillation criteria for third-order difference equations with impulses. J. Comput. Appl. Math. 225, 80–86 (2009)

    Article  Google Scholar 

  6. Lu, W., Ge, W.G., Zhao, Z.H.: Oscillatory criteria for third-order nonlinear difference equations with impulses. J. Comput. Appl. Math. 234, 3366–3372 (2010)

    Article  MATH  Google Scholar 

  7. Parhi, N., Tripathy, A.K.: Oscillation criteria for forced nonlinear neutral delay difference equations of first order. Differ. Equ. Dyn. Syst. 8, 81–97 (2000)

    MATH  Google Scholar 

  8. Parhi, N., Tripathy, A.K.: On asymptotic behaviour and oscillation of forced first order nonlinear neutral difference equations. Fasciculi Mathematici 32, 83–95 (2001)

    MATH  Google Scholar 

  9. Parhi, N., Tripathy, A.K.: Oscillation of a class of neutral difference equations of first order. J. Differ. Equ. Appl. 9, 933–946 (2003)

    Article  MATH  Google Scholar 

  10. Samoilenko, A.M., Perestynk, N.A.: Differential Equations with Impulse Effect. Visca Skola, Kiev (1987)

    Google Scholar 

  11. Tripathy, A.K.: Oscillation criteria for a class of first order neutral impulsive differential-difference equations. J. Appl. Anal. Comput. 4, 89–101 (2014)

    MATH  Google Scholar 

  12. Tripathy, A.K., Chhatria, G.N.: On oscillatory first order neutral impulsive difference equations. Math. Bohem. (2019). https://doi.org/10.21136/MB.2019.0002-18

    Article  MATH  Google Scholar 

  13. Tripathy, A.K., Chhatria, G.N.: Oscillation criteria for forced first order nonlinear neutral impulsive difference system. Tatra Mt. Math. Publ. 71, 175–193 (2018)

    MATH  Google Scholar 

  14. Wei, G.P.: The persistance of nonoscillatory solutions of difference equation under impulsive perturbations. Comput. Math. Appl. 50, 1579–1586 (2005)

    Article  MATH  Google Scholar 

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Acknowledgements

The authors are thankful to the referee for his/her valuable comments and suggestions about this work.

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  1. Department of Mathematics, Sambalpur University, Sambalpur, 768019, India

    A. K. Tripathy & G. N. Chhatria

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  1. A. K. Tripathy
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  2. G. N. Chhatria
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Correspondence to A. K. Tripathy.

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This work is supported by Rajiv Gandhi National fellowship (UGC), New Delhi, India, through the Letter no. F1-17.1/2017-18/RGNF-2017-18-SC-ORI-35849, dated. 11th July, 2017.

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Tripathy, A.K., Chhatria, G.N. Oscillation Criteria for First Order Neutral Impulsive Difference Equations with Constant Coefficients. Differ Equ Dyn Syst 31, 209–222 (2023). https://doi.org/10.1007/s12591-019-00495-7

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