{"title":"一类二阶非线性微分方程两点边值问题正解的先验估计","authors":"É. Abduragimov","doi":"10.31029/demr.11.5","DOIUrl":null,"url":null,"abstract":"A priori estimates of the positive solution of the two-point boundary value problem are obtained $y^{\\prime\\prime}=-f(x,y)$, $0<x<1$, $y(0)=y(1)=0$ assuming that $f(x,y)$ is continuous at $x \\in [0,1]$, $y \\in R$ and satisfies the condition $a_0 x^{\\gamma}y^p \\leq f(x,y) \\leq a_1 y^p$, where $a_0>0$, $a_1>0$, $p>1$, $\\gamma \\geq 0$ -- constants.","PeriodicalId":431345,"journal":{"name":"Daghestan Electronic Mathematical Reports","volume":"357 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A priori estimates of the positive solution of the two-point boundary value problem for one second-order nonlinear differential equation\",\"authors\":\"É. Abduragimov\",\"doi\":\"10.31029/demr.11.5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A priori estimates of the positive solution of the two-point boundary value problem are obtained $y^{\\\\prime\\\\prime}=-f(x,y)$, $0<x<1$, $y(0)=y(1)=0$ assuming that $f(x,y)$ is continuous at $x \\\\in [0,1]$, $y \\\\in R$ and satisfies the condition $a_0 x^{\\\\gamma}y^p \\\\leq f(x,y) \\\\leq a_1 y^p$, where $a_0>0$, $a_1>0$, $p>1$, $\\\\gamma \\\\geq 0$ -- constants.\",\"PeriodicalId\":431345,\"journal\":{\"name\":\"Daghestan Electronic Mathematical Reports\",\"volume\":\"357 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Daghestan Electronic Mathematical Reports\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31029/demr.11.5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Daghestan Electronic Mathematical Reports","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31029/demr.11.5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A priori estimates of the positive solution of the two-point boundary value problem for one second-order nonlinear differential equation
A priori estimates of the positive solution of the two-point boundary value problem are obtained $y^{\prime\prime}=-f(x,y)$, $00$, $a_1>0$, $p>1$, $\gamma \geq 0$ -- constants.
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