{"title":"时间尺度上二阶非线性阻尼动力方程的振动性","authors":"Fanfan Li, Z. Han","doi":"10.30538/psrp-oma2018.0019","DOIUrl":null,"url":null,"abstract":"In this paper, we use Riccati transformation technique to establish some new oscillation criteria for the second order nonlinear dynamic equation with damping on time scales (r(t)(x(t))) − p(t)(x(t)) + q(t)f(x(t)) = 0. Our results not only generalize some existing results, but also can be applied to the oscillation problems that are not covered in literature. Finally, we give some examples to illustrate our main results. Mathematics Subject Classification: 26E70, 34C10.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Oscillation Behavior of Second Order Nonlinear Dynamic Equation with Damping on Time Scales\",\"authors\":\"Fanfan Li, Z. Han\",\"doi\":\"10.30538/psrp-oma2018.0019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we use Riccati transformation technique to establish some new oscillation criteria for the second order nonlinear dynamic equation with damping on time scales (r(t)(x(t))) − p(t)(x(t)) + q(t)f(x(t)) = 0. Our results not only generalize some existing results, but also can be applied to the oscillation problems that are not covered in literature. Finally, we give some examples to illustrate our main results. Mathematics Subject Classification: 26E70, 34C10.\",\"PeriodicalId\":52741,\"journal\":{\"name\":\"Open Journal of Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Open Journal of Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30538/psrp-oma2018.0019\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Journal of Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30538/psrp-oma2018.0019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Oscillation Behavior of Second Order Nonlinear Dynamic Equation with Damping on Time Scales
In this paper, we use Riccati transformation technique to establish some new oscillation criteria for the second order nonlinear dynamic equation with damping on time scales (r(t)(x(t))) − p(t)(x(t)) + q(t)f(x(t)) = 0. Our results not only generalize some existing results, but also can be applied to the oscillation problems that are not covered in literature. Finally, we give some examples to illustrate our main results. Mathematics Subject Classification: 26E70, 34C10.
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