On the well posed solutions for nonlinear second order neutral difference equations

TL;DR

This paper investigates the existence, uniqueness, and parameter dependence of solutions for nonlinear second order neutral difference equations using Darbo's fixed point theorem.

Contribution

It introduces a new approach applying Darbo's fixed point theorem to analyze solutions of second order neutral nonlinear difference equations.

Findings

Established conditions for existence of solutions

Proved uniqueness under certain parameters

Analyzed how solutions depend on parameters

Abstract

In this work we investigate the existence of solutions, their uniqueness and finally dependence on parameters for solutions of second order neutral nonlinear difference equations. The main tool which we apply is Darbo fixed point theorem.