{"title":"New Oscillation Criteria for Half-Linear Second-Order Neutral Advanced Difference Equations","authors":"P. Selvakumar, P. Gopalakrishnan, A. Murugesan","doi":"10.37622/ijde/16.1.2021.107-122","DOIUrl":null,"url":null,"abstract":"We obtained oscillation criteria for the second-order half-linear neutral advanced difference equations of the kind ∆(α(ζ)(∆w(ζ))) + η(ζ)y(ζ + κ) = 0; ζ ≥ ζ0, where w(ζ) = y(ζ) + p(ζ)y(ζ + ξ). We provide a new oscillation condition, which significantly improves the existing ones, by providing a new axiom bound for a non-oscillatory solution. The derived oscillation constant is unimprovable in a certain nonneutral case. 2020 Mathematics Subject Classifications: 39A12, 39A13, 39A21.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"1 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Difference Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37622/ijde/16.1.2021.107-122","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
Abstract
We obtained oscillation criteria for the second-order half-linear neutral advanced difference equations of the kind ∆(α(ζ)(∆w(ζ))) + η(ζ)y(ζ + κ) = 0; ζ ≥ ζ0, where w(ζ) = y(ζ) + p(ζ)y(ζ + ξ). We provide a new oscillation condition, which significantly improves the existing ones, by providing a new axiom bound for a non-oscillatory solution. The derived oscillation constant is unimprovable in a certain nonneutral case. 2020 Mathematics Subject Classifications: 39A12, 39A13, 39A21.
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