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A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n) = −p(n)x(n − k) with a Positive Coefficient

Author

Listed:
  • J. Baštinec
  • L. Berezansky
  • J. Diblík
  • Z. Šmarda

Abstract

A linear (k + 1)th‐order discrete delayed equation Δx(n) = −p(n)x(n − k) where p(n) a positive sequence is considered for n → ∞. This equation is known to have a positive solution if the sequence p(n) satisfies an inequality. Our aim is to show that, in the case of the opposite inequality for p(n), all solutions of the equation considered are oscillating for n → ∞.

Suggested Citation

  • J. Baštinec & L. Berezansky & J. Diblík & Z. Šmarda, 2011. "A Final Result on the Oscillation of Solutions of the Linear Discrete Delayed Equation Δx(n) = −p(n)x(n − k) with a Positive Coefficient," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:586328
    DOI: 10.1155/2011/586328
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    References listed on IDEAS

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    1. Jaromír Baštinec & Leonid Berezansky & Josef Diblík & Zdeněk Šmarda, 2010. "On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    2. Jaromír Baštinec & Leonid Berezansky & Josef Diblík & Zdeněk Šmarda, 2010. "On the Critical Case in Oscillation for Differential Equations with a Single Delay and with Several Delays," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-20, September.
    3. G. Ladas & Ch. G. Philos & Y. G. Sficas, 1989. "Sharp conditions for the oscillation of delay difference equations," International Journal of Stochastic Analysis, Hindawi, vol. 2, pages 1-11, January.
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    Cited by:

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    3. Zeqing Liu & Shin Min Kang & Young Chel Kwun, 2012. "Positive Solutions and Iterative Approximations for a Nonlinear Two‐Dimensional Difference System with Multiple Delays," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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