Asymptotic properties of solutions to discrete Sturm-Liouville monotone type equations

Abstract

We investigate the discrete equations of the form
\[
\Delta(r_n\Delta x_n)=a_nf(x_{\sigma(n)})+b_n.
\]
Using Knaster-Tarski fixed point theorem, we study solutions with prescribed asymptotic behavior.
Our technique allows us to control the degree of approximation. In particular, we present the results
concerning harmonic and geometric approximations of solutions.