{"title":"半线性二阶中立型高级差分方程的新振动判据","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":"{\"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}","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}
New Oscillation Criteria for Half-Linear Second-Order Neutral Advanced Difference Equations
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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