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

Migda, Janusz; Schmeidel, Ewa

doi:10.2478/tmmp-2023-0014

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.

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

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