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Oscillation and stability of nonlinear neutral impulsive delay differential equations

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Abstract

In this paper, oscillation and stability of nonlinear neutral impulsive delay differential equation are studied. The main result of this paper is that oscillation and stability of nonlinear impulsive neutral delay differential equation are equivalent to oscillation and stability of corresponding nonimpulsive neutral delay differential equations. At last, two examples are given to illustrate the importance of this study.

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References

  1. D. Bainov, M. Dimitrova and A. Dishieco,Oscillation of the solution of impulsive differential equations and inequalities with retarded argument, Rocky Mountain J. Math.28 (1998), 25–40.

    Article  MATH  MathSciNet  Google Scholar 

  2. K. Gopalsamy, B. Lalli and B. Zhang,Oscillation of odd order neutral differential equations, Czch. Math. J.42 (1992), 313–323.

    MATH  MathSciNet  Google Scholar 

  3. W. Li,Positive solution of an odd order neutral delay differential equations, Nonlinear Anal.36 (1999), 899–913.

    Article  MATH  MathSciNet  Google Scholar 

  4. X. Tang, J. Yu,Oscillation and existence of positive solutions for odd order neutral equations with “integrally small” coefficients, J. Math. Anal. Appl.222 (1998), 286–296.

    Article  MATH  MathSciNet  Google Scholar 

  5. J. Yan,Oscillation of neutral impulsive delay differential equation, Chin. Ann. Math.21A (2000), 755–762.

    Google Scholar 

  6. J. Yu,The first onler differential inequalities with deviating arguments, Acta. Math. Sinica33 (1992), 152–159.

    Google Scholar 

  7. B. Zhang, B. Yang,New approach of studying the oscillation of neutral differential equations, Funkcial Ekavac,41:1 (1998), 79–89.

    MATH  Google Scholar 

  8. Y. Zhang, X. Dang,Oscillation of neutral implsive delay differential equation, Acta. Math. Sinica.41 (1998), 219–224.

    MATH  MathSciNet  Google Scholar 

  9. G. Zhang,Eventually positive Solution of odd order neutral differential equations, Appl. Math. Lett.13 (2000), 55–61.

    Article  MATH  Google Scholar 

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This work is supported by NNSF of China (No. 19831030)

Yongrui duan received her master's degree from Shanxi University and is now studying in Shanghai Jiao Tong University for Ph. D. Her research interests focus on Functional differential equation, Optimization and Cybernetics.

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Duan, Y., Tian, P. & Zhang, S. Oscillation and stability of nonlinear neutral impulsive delay differential equations. JAMC 11, 243–253 (2003). https://doi.org/10.1007/BF02935734

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  • DOI: https://doi.org/10.1007/BF02935734

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