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Asymptotic properties of solutions to difference equations of Sturm–Liouville type

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  • Migda, Janusz
  • Nockowska-Rosiak, Magdalena

Abstract

We consider the discrete Sturm–Liouville type equation of the form Δ(rnΔxn)=anf(xσ(n))+bn.Assume s is a given nonpositive real number. We present sufficient conditions for the existence of solution x with the asymptotic behavior xn=c(r1−1+⋯+rn−1−1)+d+o(ns)where c, d are given real numbers. Moreover, we establish conditions under which for a given solution x there exist real numbers c, d such that x has the above asymptotic behavior.

Suggested Citation

  • Migda, Janusz & Nockowska-Rosiak, Magdalena, 2019. "Asymptotic properties of solutions to difference equations of Sturm–Liouville type," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 126-137.
    • Handle: RePEc:eee:apmaco:v:340:y:2019:i:c:p:126-137
    DOI: 10.1016/j.amc.2018.08.001
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    References listed on IDEAS

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    1. Migda, Janusz, 2015. "Approximative solutions to difference equations of neutral type," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 763-774.
    2. Martin Bohner & Stevo Stevic, 2007. "Trench's Perturbation Theorem for Dynamic Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2007, pages 1-11, January.
    3. Migda, Janusz, 2016. "Asymptotically polynomial solutions to difference equations of neutral type," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 16-27.
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    Cited by:

    1. Migda, Janusz & Migda, Małgorzata & Zba̧szyniak, Zenon, 2019. "Asymptotically periodic solutions of second order difference equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 181-189.

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    1. Migda, Janusz, 2016. "Asymptotically polynomial solutions to difference equations of neutral type," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 16-27.

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