Necessary and sufficient conditions for solvability of the Hartman-Wintner problem for difference equations

TL;DR

This paper investigates the conditions under which the Hartman-Wintner problem for second-order difference equations can be solved, focusing on asymptotic behavior of solutions as the argument approaches infinity.

Contribution

It establishes necessary and sufficient conditions for the solvability of the Hartman-Wintner problem in the context of second-order difference equations.

Findings

Derived explicit criteria for solvability.

Analyzed asymptotic properties of solutions.

Extended classical results to difference equations.

Abstract

For homogeneous difference equation of the second order we study the analogy of Hartman-Wintner problem on asymptotic integration of fundamental system of solutions as argument tends to infinity.