{"title":"具有几个次线性中立项的二阶时滞差分方程的新振荡条件","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":"{\"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}","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}
New Oscillation Conditions for Second-Order Delay Difference Equations with Several Sub-Linear Neutral Terms
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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