{"title":"非线性时滞微分方程的振动定理","authors":"R. S. Dahiya","doi":"10.5036/BFSIU1968.14.13","DOIUrl":null,"url":null,"abstract":"First, an oscillation theorem is presented for the n-th order delay differential equation\\[ (r(t)x'(t))(n-1)+∑k_{i=1}fi(t)Fi(xτ_i(t), x'τ_i(t), ..., x(n-1)τ_i(t))=b(t), \\ \\ r(t)>0.\\]Then the asymptotic behavior of bounded oscillatory solutions of the above equations is investigated.","PeriodicalId":141145,"journal":{"name":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","volume":"40 3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1982-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Oscillation Theorems for Non-liner Delay Differential Equations\",\"authors\":\"R. S. Dahiya\",\"doi\":\"10.5036/BFSIU1968.14.13\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"First, an oscillation theorem is presented for the n-th order delay differential equation\\\\[ (r(t)x'(t))(n-1)+∑k_{i=1}fi(t)Fi(xτ_i(t), x'τ_i(t), ..., x(n-1)τ_i(t))=b(t), \\\\ \\\\ r(t)>0.\\\\]Then the asymptotic behavior of bounded oscillatory solutions of the above equations is investigated.\",\"PeriodicalId\":141145,\"journal\":{\"name\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"volume\":\"40 3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1982-05-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5036/BFSIU1968.14.13\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5036/BFSIU1968.14.13","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Oscillation Theorems for Non-liner Delay Differential Equations
First, an oscillation theorem is presented for the n-th order delay differential equation\[ (r(t)x'(t))(n-1)+∑k_{i=1}fi(t)Fi(xτ_i(t), x'τ_i(t), ..., x(n-1)τ_i(t))=b(t), \ \ r(t)>0.\]Then the asymptotic behavior of bounded oscillatory solutions of the above equations is investigated.
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