{"title":"希勒-温特纳比较定理的改进和半线性微分方程的新非振荡标准","authors":"Jaroslav Jaroš","doi":"10.1007/s00605-024-01949-z","DOIUrl":null,"url":null,"abstract":"<p>A refinement of the Hille–Wintner comparison theorem is obtained for two half-linear differential equations of the second order. As a consequence, some new nonoscillation tests for such equations are derived by means of this improved comparison technique. In most of our results coefficients and their integrals do not need to be nonnegative and are allowed to oscillate in any neighborhood of infinity.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":"27 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A refinement of the Hille–Wintner comparison theorem and new nonoscillation criteria for half-linear differential equations\",\"authors\":\"Jaroslav Jaroš\",\"doi\":\"10.1007/s00605-024-01949-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A refinement of the Hille–Wintner comparison theorem is obtained for two half-linear differential equations of the second order. As a consequence, some new nonoscillation tests for such equations are derived by means of this improved comparison technique. In most of our results coefficients and their integrals do not need to be nonnegative and are allowed to oscillate in any neighborhood of infinity.</p>\",\"PeriodicalId\":18913,\"journal\":{\"name\":\"Monatshefte für Mathematik\",\"volume\":\"27 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-02-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Monatshefte für Mathematik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00605-024-01949-z\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-024-01949-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A refinement of the Hille–Wintner comparison theorem and new nonoscillation criteria for half-linear differential equations
A refinement of the Hille–Wintner comparison theorem is obtained for two half-linear differential equations of the second order. As a consequence, some new nonoscillation tests for such equations are derived by means of this improved comparison technique. In most of our results coefficients and their integrals do not need to be nonnegative and are allowed to oscillate in any neighborhood of infinity.
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