{"title":"一阶时滞微分方程的振动理论","authors":"Y. Shoukaku","doi":"10.18311/JIMS/2019/19834","DOIUrl":null,"url":null,"abstract":"In this paper we try to improve the conditions of [4]. Consequently, we introduce that L>e-1/e-2(k + 1/λ 1 ) - 1/e-2 is a sufficient condition for the oscillation of all solutions of first order delay differential equation x′(t) + p(t)x(σ(t)) = 0 under the conditions L < 1 and 0 < k </1/e, where k=liminf t→∞ ∫ t σ(t) p(s)ds, L=limsup t→∞ ∫ t σ(t) p(s)ds and λ 1 is the smaller root of the equation λ=e kλ","PeriodicalId":38246,"journal":{"name":"Journal of the Indian Mathematical Society","volume":"86 1","pages":"315-324"},"PeriodicalIF":0.0000,"publicationDate":"2019-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Oscillation Theory of First Order Differential Equations with Delay\",\"authors\":\"Y. Shoukaku\",\"doi\":\"10.18311/JIMS/2019/19834\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we try to improve the conditions of [4]. Consequently, we introduce that L>e-1/e-2(k + 1/λ 1 ) - 1/e-2 is a sufficient condition for the oscillation of all solutions of first order delay differential equation x′(t) + p(t)x(σ(t)) = 0 under the conditions L < 1 and 0 < k </1/e, where k=liminf t→∞ ∫ t σ(t) p(s)ds, L=limsup t→∞ ∫ t σ(t) p(s)ds and λ 1 is the smaller root of the equation λ=e kλ\",\"PeriodicalId\":38246,\"journal\":{\"name\":\"Journal of the Indian Mathematical Society\",\"volume\":\"86 1\",\"pages\":\"315-324\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-08-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Indian Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18311/JIMS/2019/19834\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Indian Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18311/JIMS/2019/19834","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Oscillation Theory of First Order Differential Equations with Delay
In this paper we try to improve the conditions of [4]. Consequently, we introduce that L>e-1/e-2(k + 1/λ 1 ) - 1/e-2 is a sufficient condition for the oscillation of all solutions of first order delay differential equation x′(t) + p(t)x(σ(t)) = 0 under the conditions L < 1 and 0 < k
期刊介绍：
The Society began publishing Progress Reports right from 1907 and then the Journal from 1908 (The 1908 and 1909 issues of the Journal are entitled "The Journal of the Indian Mathematical Club"). From 1910 onwards,it is published as its current title ''the Journal of Indian Mathematical Society. The four issues of the Journal constitute a single volume and it is published in two parts: issues 1 and 2 (January to June) as one part and issues 3 and 4 (July to December) as the second part. The four issues of the Mathematics Student (another periodical of the Society) are published as a single yearly volume. Only the original research papers of high quality are published in the Journal of Indian Mathematical Society.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
