Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Existence of a unique bounded solution to a linear second-order difference equation and the linear first-order difference equation
Journal: Advances in Difference Equations
Issue Date: 15-Jun-2017
Rank: M21
ISSN: 1687-1847
DOI: 10.1186/s13662-017-1227-x
Abstract: 
We present some interesting facts connected with the following second-order difference equation:
xn+2−qnxn=fn,n∈N0,
where (qn)n∈N0 and (fn)n∈N0 are given sequences of numbers. We give some sufficient conditions for the existence of a unique bounded solution to the difference equation and present an elegant proof based on a combination of theory of linear difference equations and the Banach fixed point theorem. We also deal with the equation by using theory of solvability of difference equations. A global convergence result of solutions to a linear first-order difference equation is given. Some comments on an abstract version of the linear first-order difference equation are also given.
Publisher: Springer Link

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