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Criticality of general two‐term even‐order linear difference equation via a chain of recessive solutions

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  • Jan Jekl

Abstract

In this paper, the author investigates particular disconjugate even‐order linear difference equations with two terms and classify them based on the properties of their recessive solutions at plus and minus infinity. The main theorem described states that the studied equation is (k−p+1)$(k-p+1)$‐critical whenever a specific second‐order linear difference equation is p$p$‐critical. In the proof, the author derived closed‐form solutions for the studied equation wherein the solutions of the said second‐order equation appear. Furthermore, the solutions were organized, in order to determine recessive solutions, into a linear chain by sequence ordering that compares the solutions at ±∞$\pm \infty$.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:8:p:2970-2985
    DOI: 10.1002/mana.202300090
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    References listed on IDEAS

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    1. Ignacio Márquez Albés & Giselle A. Monteiro, 2021. "Notes on the existence and uniqueness of solutions of Stieltjes differential equations," Mathematische Nachrichten, Wiley Blackwell, vol. 294(4), pages 794-814, April.
    2. 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.
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