Startseite Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale
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Oscillation criteria for quasi-linear neutral delay dynamic equations on time scale

  • Qiaoshun Yang EMAIL logo , Zhiting Xu und Ping Long
Veröffentlicht/Copyright: 28. April 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 1

Abstract

In this paper, we consider the oscillation for the second-order quasi-linear neutral dynamic equation

(r(t)|ZΔ(t)|α−1ZΔ(t))Δ+q(t)|x(δ(t))|β−1x(δ(t))=0.

on time scale 𝕋, where Z(t) = x(t) + p(t)x(τ(t)), α,β > 0 are constants. We establish some new oscillation criteria and give sufficient conditions to insure that all solutions of quasi-linear neutral dynamic equation are oscillatory on time scale 𝕋. The new oscillation criteria are presented that improve some known results in the literature.

Key words: oscillation; neutral dynamic equation; time scale
MSC: Primary 34K11; 34C10; 39A11; 34C15

This project was supported by Foundation of Hunan Educational Committee (Grant No. 13C753).

Acknowledgement

We are grateful to the anonymous referees for their careful reading and helpful comments which led to an improvement of our original manuscript.

  1. This paper has been communicated by Michal Fečkan

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Received: 2013-7-24
Accepted: 2013-10-5
Published Online: 2016-4-28
Published in Print: 2016-2-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0128
Schlagwörter für diesen Artikel
oscillation; neutral dynamic equation; time scale

Artikel in diesem Heft

  1. Research Article
  2. Prof. RNDr. Ján Jakubík, DrSc. passed away
  3. Research Article
  4. On the number of slim, semimodular lattices
  5. Research Article
  6. Quantum computational algebra with a non-commutative generalization
  7. Research Article
  8. Lexico groups and direct products of lattice ordered groups
  9. Research Article
  10. Values of limit periodic sequences and functions
  11. Research Article
  12. On representation of quasi-Hopf group coalgebras
  13. Research Article
  14. On the q-Bernstein polynomials of the logarithmic function in the case q > 1
  15. Research Article
  16. On some modification of Darboux property
  17. Research Article
  18. Separating sets by peripherally continuous functions
  19. Research Article
  20. Persistence and extinction of a stochastic delay predator-prey model in a polluted environment
  21. Research Article
  22. On O’Malley preponderantly continuous functions
  23. Research Article
  24. Inequalities for the normalized Jensen functional with applications
  25. Research Article
  26. Majorization of starlike and convex functions of complex order involving linear operators
  27. Research Article
  28. Fekete–Szegö problem for some starlike functions related to shell-like curves
  29. Research Article
  30. Central functions for classes of concave univalent functions
  31. Research Article
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