Qin Diao , Yong-Guo Shi , Hari Mohan Srivastava , Babak Shiri , Kelin Li
{"title":"Asymptotic analysis of solutions of delay difference equations","authors":"Qin Diao , Yong-Guo Shi , Hari Mohan Srivastava , Babak Shiri , Kelin Li","doi":"10.1016/j.rinam.2025.100562","DOIUrl":null,"url":null,"abstract":"<div><div>The asymptotic behavior of solutions for the delay difference equation <span><math><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><mo>=</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></msub><mi>f</mi><mrow><mo>(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>k</mi></mrow></msub><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mspace></mspace><mi>n</mi><mo>></mo><mi>k</mi><mo>,</mo><mspace></mspace><mspace></mspace><mtext>for some</mtext><mspace></mspace><mspace></mspace><mi>k</mi><mo>∈</mo><mi>N</mi><mo>,</mo></mrow></math></span> is investigated, where <span><math><mi>f</mi></math></span> has an asymptotic power series. These equations have been studied for some special cases. This paper analyzes other cases and presents asymptotic expansions of solutions for such higher-order difference equations. Several examples are provided.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100562"},"PeriodicalIF":1.3000,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590037425000263","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/3/16 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
The asymptotic behavior of solutions for the delay difference equation is investigated, where has an asymptotic power series. These equations have been studied for some special cases. This paper analyzes other cases and presents asymptotic expansions of solutions for such higher-order difference equations. Several examples are provided.
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