Modified Oscillation Results for Advanced Difference Equations of Second-Order

J. Appl. Math. Pub Date : 2022-06-30 DOI:10.1155/2022/3407776

G. Chatzarakis, N. Indrajith, S. Panetsos, E. Thandapani

{"title":"Modified Oscillation Results for Advanced Difference Equations of Second-Order","authors":"G. Chatzarakis, N. Indrajith, S. Panetsos, E. Thandapani","doi":"10.1155/2022/3407776","DOIUrl":null,"url":null,"abstract":"In this paper, we present a new method to establish the oscillation of advanced second-order difference equations of the form \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\n <mi>Δ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>η</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n <mi>Δ</mi>\n <mi>υ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n </mrow>\n </mfenced>\n <mo>+</mo>\n <mi>ρ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n <mi>υ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>σ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n </mrow>\n </mfenced>\n <mo>=</mo>\n <mn>0</mn>\n <mo>,</mo>\n </math>\n using the ordinary difference equation \n <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\n <mi>Δ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>η</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n <mi>Δ</mi>\n <mi>υ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n </mrow>\n </mfenced>\n <mo>+</mo>\n <mi>q</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n </mrow>\n </mfenced>\n <mi>υ</mi>\n <mfenced open=\"(\" close=\")\">\n <mrow>\n <mi>ℓ</mi>\n <mo>+</mo>\n <mn>1</mn>\n </mrow>\n </mfenced>\n <mo>=</mo>\n <mn>0</mn>\n <mo>.</mo>\n </math>\n The obtained results are new and improve the existing criteria. We provide examples to illustrate the main results.","PeriodicalId":14766,"journal":{"name":"J. Appl. Math.","volume":"11 1","pages":"3407776:1-3407776:5"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"J. Appl. Math.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2022/3407776","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}