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Boundedness of Nonlinear Differential Systems with Impulsive Effect on Random Moments

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Abstract

The model of nonlinear differential systems with impulsive effect on random moments is brought forward in this paper. Then, sufficient conditions for (uniform, uniform and ultimate, and uniform and uniformly ultimate) p−moment boundedness of the systems are presented. Finally, an example is discussed to show applications of two obtained results.

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References

  1. Akhmetov, M.U., Zafer, A. Stability of the zero solution of impulsive differential equations by the Liapunov second method. Journal of Mathematical Analysis and Aplications, 248: 69–82 (2000)

    Article  MathSciNet  Google Scholar 

  2. Akhmetov, M.U., Zafer, A. Successive approximation method for quasilinear impulsive differential equations with control. Applied Mathematics Letters, 13: 99–105 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bainov, D.D., Simeonov, P.S. Differentiability of solutions of systems with impulsive effect with respect to initial data and parameter. Bull. Inst. Math. Acad. Sci., 15: 251–269 (1987)

    MATH  Google Scholar 

  4. Bainov, D.D., Simeonov, P.S. Systems with impulsive effect. In: Stability Theory and Applications, Chichester, UK: Ellis Horwood, 1989

  5. Cooke, C.H., Kroll, J. The existence of periodic solutions to certain impulsive differential equations. Computers and Mathematics with Applications, 44: 667–676 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Covachev, V., Akca, H., Yenicerioglu, F. Difference approximations for impulsive differential equations. Applied Mathematics and Computation, 121: 383–390 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  7. Kou, C.H., Zhang, S.N., Wu, S.J. Stability analysis in terms of two measures for impulsive differential equations. J. London Math. Soc., 66: 142–152 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lakshmikantham, V., Bainov, D.D., Simeonov, P.S. Theory of Impulsive Differntial Equations. World Scientific, Singapore, 1989

  9. Pinto, M. Asymptotic behavior of differential systems with impulse effect. Nonlinear Analysis, 30: 1133–1140 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  10. Soliman, A.A. On stability of perturbed impulsive differential systems. Applied Mathematics and Computation, 133: 105–117 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  11. Soliman, A.A. Stability criteria of impulsive differential systems. Applied Mathematics and Computation 134: 445–457 (2003)

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Statistics, East China Normal University, Shanghai 200062, China

    Shu-jin Wu

  2. Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China

    Xian-zhang Meng

Authors
  1. Shu-jin Wu
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  2. Xian-zhang Meng
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Correspondence to Xian-zhang Meng.

Additional information

Partially supported by the NNSF of China (No. 19831030, No. 10371074).

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Wu, Sj., Meng, Xz. Boundedness of Nonlinear Differential Systems with Impulsive Effect on Random Moments. Acta Mathematicae Applicatae Sinica, English Series 20, 147–154 (2004). https://doi.org/10.1007/s10255-004-0157-z

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  • DOI: https://doi.org/10.1007/s10255-004-0157-z

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