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

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.

Language:: English

Publication timeframe:: 3 times per year
Journal Subjects:: Mathematics, General Mathematics

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

Janusz Migda

Ewa Schmeidel

Published Online: Jun 28, 2023

Page range: 35 - 44

Received: Nov 14, 2022

DOI: https://doi.org/10.2478/tmmp-2023-0014

KeywordsSturm-Liouville difference equation, prescribed asymptotic behaviour, convergent solution, asymptotically periodic solution, degree of approximation

© 2023 Janusz Migda et al., published by Sciendo

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Keywords
Sturm-Liouville difference equation, prescribed asymptotic behaviour, convergent solution, asymptotically periodic solution, degree of approximation