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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