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.

Język:: Angielski

Częstotliwość wydawania:: 3 razy w roku
Dziedziny czasopisma:: Matematyka, Matematyka ogólna

Kanał RSS czasopisma

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

Janusz Migda

Ewa Schmeidel

Data publikacji: 28 cze 2023

Zakres stron: 35 - 44

Otrzymano: 14 lis 2022

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

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

© 2023 Janusz Migda et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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