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

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

By: Janusz Migda and  Ewa Schmeidel  
Open Access
|Jun 2023

Abstract

We investigate the discrete equations of the form Δ(rnΔxn)=anf(xσ(n))+bn. \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.

DOI: https://doi.org/10.2478/tmmp-2023-0014 | Journal eISSN: 1338-9750 | Journal ISSN: 12103195
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: 3 issues per year

© 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.