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Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients

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  • Petr Hasil
  • Michal Veselý

Abstract

We investigate a type of the Sturm‐Liouville difference equations with almost periodic coefficients. We prove that there exists a constant, which is the borderline between the oscillation and the nonoscillation of these equations. We compute this oscillation constant explicitly. If the almost periodic coefficients are replaced by constants, our result reduces to the well‐known result about the discrete Euler equation.

Suggested Citation

  • Petr Hasil & Michal Veselý, 2012. "Critical Oscillation Constant for Difference Equations with Almost Periodic Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:471435
    DOI: 10.1155/2012/471435
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    References listed on IDEAS

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    1. Constantin Corduneanu, 2009. "Almost Periodic Oscillations and Waves," Springer Books, Springer, number 978-0-387-09819-7, March.
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    Cited by:

    1. Petr Hasil & Robert Mařík & Michal Veselý, 2014. "Conditional Oscillation of Half‐Linear Differential Equations with Coefficients Having Mean Values," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Jan Jekl, 2024. "Criticality of general two‐term even‐order linear difference equation via a chain of recessive solutions," Mathematische Nachrichten, Wiley Blackwell, vol. 297(8), pages 2970-2985, August.

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