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

  • Yaşar Bolat EMAIL logo und Ömer Akin 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, oscillation criteria are obtained for higher-order half-linear delay difference equations involving generalized difference operator of the form

Δb(pn(Δbm−1xn)α)+qnxn−σβ=0,  n≥n0,

where ∆b is defined by ∆byn = yn+1 - byn, b ∈ ℝ - {0}, p: ℕ → ℝ+, α, β are the ratio of odd positive integers with β ≤ α; m, n, n0, σ are non-negative integers, q: ℕ → ℝ. The cases of b negative and positive and qn ≥ 0, which has important role for oscillation of this equation, are considered. Also we provide some examples to illustrate our main results.

Key words: oscillation; difference equaions; generalized difference; half-linear difference equation
MSC 2010: Primary 39A10

(Communicated by Michal Fečkan)

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Received: 2012-11-14
Accepted: 2013-12-9
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-2015-0169
Schlagwörter für diesen Artikel
oscillation; difference equaions; generalized difference; half-linear difference equation

Artikel in diesem Heft

  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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  23. Research Article
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  28. On the solutions of a fourth order parabolic equation modeling epitaxial thin film growth
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  34. Multiplier spaces and the summing operator for series
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