Asymptotic Properties of Solutions to Discrete Sturm-Liouville Monotone Type Equations

Janusz Migda; Ewa Schmeidel

doi:10.2478/tmmp-2023-0014

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Asymptotic Properties of Solutions to Discrete Sturm-Liouville Monotone Type Equations

Tatra Mountains Mathematical Publications

Volume 84 (2023): Issue 2 (June 2023)

By: Janusz Migda and Ewa Schmeidel

Open Access

|Jun 2023

Abstract

We investigate the discrete equations of the form $Δ (r_{n} Δ x_{n}) = a_{n} f (x_{σ (n)}) + b_{n} .$ \Delta \left( {{r_n}\Delta {x_n}} \right) = {a_n}f\left( {{x_{\sigma \left( n \right)}}} \right) + {b_n}. Using the Knaster-Tarski fixed point theorem, we study solutions with prescribed asymptotic behaviour. Our technique allows us to control the degree of approximation. In particular, we present the results concerning harmonic and geometric approximations of solutions.

References

Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2023-0014 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 35 - 44

Submitted on: Nov 14, 2022

Published on: Jun 28, 2023

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

Sturm-Liouville difference equation,

prescribed asymptotic behaviour,

convergent solution,

asymptotically periodic solution,

degree of approximation

Related subjects:

Mathematics,

General mathematics

© 2023 Janusz Migda, Ewa Schmeidel, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 84 (2023): Issue 2 (June 2023)