{"title":"On the global behavior of the rational difference equation \\(y_{n+1}=\\frac{\\alpha_n+y_{n-r}}{\\alpha_n+y_{n-k}}\\)","authors":"Sihem Oudi̇na, M. Kerker, Abdelouahab Salmi","doi":"10.53006/rna.974156","DOIUrl":null,"url":null,"abstract":"In this article, we study the global behavior of the following higher-order nonautonomous rational difference equation \n\\[ \ny_{n+1}=\\frac{\\alpha_n+y_{n-r}}{\\alpha_n+y_{n-k}},\\quad n=0,1,..., \n\\] \nwhere \\(\\left\\{\\alpha_n\\right\\}_{n\\geq0}\\) is a bounded sequence of \npositive numbers, \\(k,r\\) are nonnegative integers such that \\(r","PeriodicalId":36205,"journal":{"name":"Results in Nonlinear Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Nonlinear Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.53006/rna.974156","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
In this article, we study the global behavior of the following higher-order nonautonomous rational difference equation
\[
y_{n+1}=\frac{\alpha_n+y_{n-r}}{\alpha_n+y_{n-k}},\quad n=0,1,...,
\]
where \(\left\{\alpha_n\right\}_{n\geq0}\) is a bounded sequence of
positive numbers, \(k,r\) are nonnegative integers such that \(r