{"title":"New Oscillation Conditions for Second-Order Delay Difference Equations with Several Sub-Linear Neutral Terms","authors":"C. Rajan, A. Murugesan, P. Gopalakrishnan","doi":"10.37622/ijde/16.1.2021.123-135","DOIUrl":null,"url":null,"abstract":"We derive oscillatory conditions for the second-order delay difference equation ∆ ( φ(ζ)(∆v(ζ)) ) + μ(ζ)x(η(ζ)) = 0; ζ ≥ ζ0, where v(ζ) = x(ζ) + ∑m i=1 pi(ζ)x i(κi(ζ)). We investigate oscillatory behavior for the cases when ξ > ν and ξ < ν. Many results presented in the literature are supplemented and improved by this new theorem. Finally, we give some examples to show our major findings. 2020 Mathematics Subject Classifications: 39A12, 39A13, 39A21.","PeriodicalId":36454,"journal":{"name":"International Journal of Difference Equations","volume":"53 3 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/16.1.2021.123-135","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 derive oscillatory conditions for the second-order delay difference equation ∆ ( φ(ζ)(∆v(ζ)) ) + μ(ζ)x(η(ζ)) = 0; ζ ≥ ζ0, where v(ζ) = x(ζ) + ∑m i=1 pi(ζ)x i(κi(ζ)). We investigate oscillatory behavior for the cases when ξ > ν and ξ < ν. Many results presented in the literature are supplemented and improved by this new theorem. Finally, we give some examples to show our major findings. 2020 Mathematics Subject Classifications: 39A12, 39A13, 39A21.
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