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Oscillation criteria for higher order nonlinear delay dynamic equations on time scales

  • Xin Wu und Taixiang Sun EMAIL logo
Veröffentlicht/Copyright: 26. August 2016
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Mathematica Slovaca
Aus der Zeitschrift Mathematica Slovaca Band 66 Heft 3

Abstract

In this paper, we study the oscillation criteria of the following higher order nonlinear delay dynamic equation

Rn△(t,x(t))+b(t)|Rn−1△(t,x(t))|γ−1Rn−1△(t,x(t))+q(t)f(|x(τ(t))|γ−1x(τ(t)))=0

on an arbitrary time scale T with sup T = ∞, where n ≥ 2, γ > 0 is a constant, τ: T → T with τ(t) ≤ t and limt→∞⁡τ(t)=∞ and

Rk(t,x(t))=x(t),ifk=0,rk(t)Rk−1△(t,x(t)),if1≤k≤n−1,rn(t)|Rn−1△(t,x(t))|γ−1Rn−1△(t,x(t)),ifk=n,

with rk(t) (1 ≤ k ≤ n) are positive rd-continuous functions. We give sufficient conditions under which every solution of this equation is either oscillatory or tends to zero.

MSC 2010: Primary 34K11; 39A10; 39A99
Keywords: oscillation; dynamic equation; time scale

Project Supported by NNSF of China (11461003) and NSF of Guangxi (2014GXNSFBA118003)

(Communicated by Michal Fečkan)

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Received: 2013-6-4
Accepted: 2014-1-9
Published Online: 2016-8-26
Published in Print: 2016-6-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0166
Schlagwörter für diesen Artikel
oscillation; dynamic equation; time scale

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  1. Research Article
  2. On the vertex-to-edge duality between the Cayley graph and the coset geometry of von Dyck groups
  3. Research Article
  4. Characterization of hereditarily reversible posets
  5. Research Article
  6. Families of sets which can be represented as sublattices of the lattice of convex subsets of a linearly ordered set
  7. Research Article
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  9. Research Article
  10. On the congruent number problem over integers of cyclic number fields
  11. Research Article
  12. On the Diophantine equation x2 + C= yn for C = 2a3b17c and C = 2a13b17c
  13. Research Article
  14. Representations and evaluations of the error term in a certain divisor problem
  15. Research Article
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  17. Research Article
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  19. Research Article
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  21. Research Article
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