{"title":"二阶非线性微分方程第一个零的下界","authors":"D. Biles","doi":"10.7153/dea-2018-10-13","DOIUrl":null,"url":null,"abstract":"We consider establishing lower bounds for the first zero of the solution of the nonlinear second order initial value problem (p(x)y′(x))′ + f (x,y(x)) = 0, x 0 y(0) = a > 0, y′(0) = 0. Using the linear case as a starting point, we prove several of these theorems, comparing them by considering several examples. Mathematics subject classification (2010): 34C10, 34A34, 34A36.","PeriodicalId":11162,"journal":{"name":"Differential Equations and Applications","volume":"15 3 1","pages":"209-218"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lower bounds for the first zero for nonlinear second order differential equations\",\"authors\":\"D. Biles\",\"doi\":\"10.7153/dea-2018-10-13\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider establishing lower bounds for the first zero of the solution of the nonlinear second order initial value problem (p(x)y′(x))′ + f (x,y(x)) = 0, x 0 y(0) = a > 0, y′(0) = 0. Using the linear case as a starting point, we prove several of these theorems, comparing them by considering several examples. Mathematics subject classification (2010): 34C10, 34A34, 34A36.\",\"PeriodicalId\":11162,\"journal\":{\"name\":\"Differential Equations and Applications\",\"volume\":\"15 3 1\",\"pages\":\"209-218\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/dea-2018-10-13\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/dea-2018-10-13","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
考虑建立非线性二阶初值问题(p(x)y ' (x)) ' + f (x,y(x)) = 0, x 0 y(0) = a > 0, y '(0) = 0)解的第一个零的下界。以线性情况为出发点，我们证明了其中几个定理，并通过考虑几个例子对它们进行了比较。数学学科分类(2010):34C10, 34A34, 34A36。
Lower bounds for the first zero for nonlinear second order differential equations
We consider establishing lower bounds for the first zero of the solution of the nonlinear second order initial value problem (p(x)y′(x))′ + f (x,y(x)) = 0, x 0 y(0) = a > 0, y′(0) = 0. Using the linear case as a starting point, we prove several of these theorems, comparing them by considering several examples. Mathematics subject classification (2010): 34C10, 34A34, 34A36.
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