研究二阶中立型时滞微分方程振荡的一种改进方法。

IF 1.6 3区数学 Q1 Mathematics

Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-07-27 DOI:10.1186/s13660-018-1767-y

Said R Grace, Jozef Džurina, Irena Jadlovská, Tongxing Li

{"title":"研究二阶中立型时滞微分方程振荡的一种改进方法。","authors":"Said R Grace, Jozef Džurina, Irena Jadlovská, Tongxing Li","doi":"10.1186/s13660-018-1767-y","DOIUrl":null,"url":null,"abstract":"The paper is devoted to the study of oscillation of solutions to a class of second-order half-linear neutral differential equations with delayed arguments. New oscillation criteria are established, and they essentially improve the well-known results reported in the literature, including those for non-neutral differential equations. The adopted approach refines the classical Riccati transformation technique by taking into account such part of the overall impact of the delay that has been neglected in the earlier results. The effectiveness of the obtained criteria is illustrated via examples.","PeriodicalId":49163,"journal":{"name":"Journal of Inequalities and Applications","volume":null,"pages":null},"PeriodicalIF":1.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13660-018-1767-y","citationCount":"64","resultStr":"{\"title\":\"An improved approach for studying oscillation of second-order neutral delay differential equations.\",\"authors\":\"Said R Grace, Jozef Džurina, Irena Jadlovská, Tongxing Li\",\"doi\":\"10.1186/s13660-018-1767-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper is devoted to the study of oscillation of solutions to a class of second-order half-linear neutral differential equations with delayed arguments. New oscillation criteria are established, and they essentially improve the well-known results reported in the literature, including those for non-neutral differential equations. The adopted approach refines the classical Riccati transformation technique by taking into account such part of the overall impact of the delay that has been neglected in the earlier results. The effectiveness of the obtained criteria is illustrated via examples.\",\"PeriodicalId\":49163,\"journal\":{\"name\":\"Journal of Inequalities and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1186/s13660-018-1767-y\",\"citationCount\":\"64\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Inequalities and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1186/s13660-018-1767-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2018/7/27 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Inequalities and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1186/s13660-018-1767-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2018/7/27 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 64

摘要

研究了一类二阶半线性中立型时滞参数微分方程解的振动性。建立了新的振荡判据，从本质上改进了文献中众所周知的结果，包括非中立型微分方程的结果。所采用的方法改进了经典的Riccati变换技术，考虑了在早期结果中被忽略的部分延迟的总体影响。通过算例说明了所得准则的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

An improved approach for studying oscillation of second-order neutral delay differential equations.

查看原文本刊更多论文

An improved approach for studying oscillation of second-order neutral delay differential equations.

The paper is devoted to the study of oscillation of solutions to a class of second-order half-linear neutral differential equations with delayed arguments. New oscillation criteria are established, and they essentially improve the well-known results reported in the literature, including those for non-neutral differential equations. The adopted approach refines the classical Riccati transformation technique by taking into account such part of the overall impact of the delay that has been neglected in the earlier results. The effectiveness of the obtained criteria is illustrated via examples.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.