# On discrete boundary value problems with nonlocal conditions in a quarter-plane

## TL;DR

This paper investigates discrete boundary value problems with nonlocal conditions in a quarter-plane, establishing solvability criteria and comparing discrete solutions to their continuous counterparts using Sobolev--Slobodetskii spaces.

## Contribution

It introduces a discrete analogue of pseudo-differential equations in a quarter-plane and develops solvability conditions based on wave factorization, bridging discrete and continuous solutions.

## Key findings

- Derived solvability conditions for discrete boundary value problems
- Compared discrete solutions with continuous solutions in Sobolev--Slobodetskii spaces
- Established a framework for analyzing nonlocal boundary conditions in discrete settings

## Abstract

We consider discrete analogue of model pseudo-differential equations in discrete plane sector using discrete variant of Sobolev--Slobodetskii spaces. Starting from the concept of wave factorization for elliptic periodic symbol we describe solvability conditions for the equations and corresponding discrete boundary value problems. We give also a comparison between discrete and continuous solutions in appropriate discrete normed spaces.