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Oscillation and Strong Oscillation for Impulsive Neutral Parabolic Differential Systems with Delays

  • Yu-Tian Zhang
  • Qi Luo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3645)

Abstract

In respect that, in practical systems, we usually merely consider oscillation while strong oscillation is sometimes ignored which is also of wide applied background, this paper presents some results of the oscillation and strong oscillation of impulsive neutral parabolic differential systems with delays. Some criteria on the oscillation and strong oscillation are established by using analytical techniques. It is shown that, for impulsive parabolic differential systems with delays, although strong oscillation has more restriction than oscillation, the result of strong oscillation can be parallel to that of oscillation under certain conditions.

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References

  1. 1.
    Lakshmikantham, V., Bainov, D.D., Simeonov, P.S.: Theory of Impulsive Differential Equations. World Scientific, Singapore (1989)zbMATHGoogle Scholar
  2. 2.
    Bainov, D.D., Simeonov, P.S.: Systems with Impulsive Effect: Stability, Theory and Applications. Wiley, New York (1989)Google Scholar
  3. 3.
    Bainov, D.D., Kamont, Z., Minchev, E.: Monotone Iterative Methods for Impulsive Hyperbolic Differential Functional Equations. J. Comput. Appl. Math. 70, 329–347 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Cui, B.T., Liu, Y., Deng, F.: Some Oscillation Problems for Impulsive Hyperbolic Differential Systems with Several Delays. Appl. Math. Comput. 146, 667–679 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bainov, D.D., Minchev, E.: Estimates of Solutions of Impulsive Parabolic Equations and Applications to The Population Dynamics. Publ. Math. 40, 85–94 (1996)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Erbe, L.H., Freedman, H.I., Liu, X., Wu, J.H.: Comparison Principle for Impulsive Parabolic Equations with Applications to Models of Single Species Growth. J. Austral. Math. Soc. Ser. B32, 382–400 (1991)Google Scholar
  7. 7.
    Fu, X., Liu, X., Sivaloganathan, S.: Oscillation Criteria for Impulsive Parabolic Systems. Appl. Anal. 79, 239–255 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Fu, X., Liu, X., Sivaloganathan, S.: Oscillation Criteria for Impulsive Parabolic Equations with Delays. J. Math. Anal. Appl. 268, 647–664 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Gao, W., Wang, J.: Estimates of Solutions of Impulsive Parabolic Equations under Neumann Boundary Condition. J. Math. Anal. Appl. 283, 478–490 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Luo, J.: Oscillation of Hyperbolic Partial Differential Equations with Impulses. Appl. Math. Comput. 133, 309–318 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Zhang, L.: Oscillation Criteria for Hyperbolic Partial Differential Equations with Fixed Moments of Impulse Effects. Acta. Math. Sinica. 43, 17–26 (2000)Google Scholar
  12. 12.
    Yan, J.R.: The Oscillation of Impulsive Neutral Differential Equations with Delays. Chinese Annals of Mathematics 25(2), 95–98 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Yu-Tian Zhang
    • 1
  • Qi Luo
    • 1
  1. 1.College of ScienceWuhan University of Science and TechnologyWuhanChina

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