{"title":"用李雅普诺夫函数定性分析时间尺度上的动力方程","authors":"E. Messina, Y. Raffoul, A. Vecchio","doi":"10.7153/dea-2022-14-14","DOIUrl":null,"url":null,"abstract":". We employ Lyapunov functions to study boundedness and stability of dynamic equa- tions on time scales. Most of our Lyapunov functions involve the term | x | and its Δ -derivative. In particular, we prove general theorems regarding qualitative analysis of solutions of delay dynamical systems and then use Lyapunov functionals that partially include | x | to provide ex-amples.","PeriodicalId":179999,"journal":{"name":"Differential Equations & Applications","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Qualitative analysis of dynamic equations on time scales using Lyapunov functions\",\"authors\":\"E. Messina, Y. Raffoul, A. Vecchio\",\"doi\":\"10.7153/dea-2022-14-14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We employ Lyapunov functions to study boundedness and stability of dynamic equa- tions on time scales. Most of our Lyapunov functions involve the term | x | and its Δ -derivative. In particular, we prove general theorems regarding qualitative analysis of solutions of delay dynamical systems and then use Lyapunov functionals that partially include | x | to provide ex-amples.\",\"PeriodicalId\":179999,\"journal\":{\"name\":\"Differential Equations & Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations & Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/dea-2022-14-14\",\"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 & Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/dea-2022-14-14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
. 利用李雅普诺夫函数研究了时间尺度上动态方程的有界性和稳定性。我们的大多数李雅普诺夫函数都涉及到项| x |及其Δ -导数。特别地,我们证明了关于时滞动力系统解的定性分析的一般定理,然后用部分包含x的Lyapunov泛函提供了例子。
Qualitative analysis of dynamic equations on time scales using Lyapunov functions
. We employ Lyapunov functions to study boundedness and stability of dynamic equa- tions on time scales. Most of our Lyapunov functions involve the term | x | and its Δ -derivative. In particular, we prove general theorems regarding qualitative analysis of solutions of delay dynamical systems and then use Lyapunov functionals that partially include | x | to provide ex-amples.