{"title":"具有退化平衡的标量状态相关延迟微分方程的准周期响应解","authors":"Xiaolong He, Feng Jin, Yongli Song","doi":"10.1007/s12346-024-01104-x","DOIUrl":null,"url":null,"abstract":"<p>We consider the state-dependent delay differential equation (SDDE) obtained by adding delayed perturbation to a one-dimensional ODE with a degenerate equilibrium. We prove the existence of the response solution of the equation, i.e., the quasi-periodic solution with the same frequency as the forcing. The novelty of our paper is to provide a concrete example to discuss the smoothness issues of SDDE, especially showing the analyticity of quasi-periodic solutions in some probability sense.\n</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"19 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quasi-periodic Response Solution to Scalar State-Dependent Delay Differential Equation with Degenerate Equilibrium\",\"authors\":\"Xiaolong He, Feng Jin, Yongli Song\",\"doi\":\"10.1007/s12346-024-01104-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider the state-dependent delay differential equation (SDDE) obtained by adding delayed perturbation to a one-dimensional ODE with a degenerate equilibrium. We prove the existence of the response solution of the equation, i.e., the quasi-periodic solution with the same frequency as the forcing. The novelty of our paper is to provide a concrete example to discuss the smoothness issues of SDDE, especially showing the analyticity of quasi-periodic solutions in some probability sense.\\n</p>\",\"PeriodicalId\":48886,\"journal\":{\"name\":\"Qualitative Theory of Dynamical Systems\",\"volume\":\"19 1\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Qualitative Theory of Dynamical Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s12346-024-01104-x\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Qualitative Theory of Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-024-01104-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Quasi-periodic Response Solution to Scalar State-Dependent Delay Differential Equation with Degenerate Equilibrium
We consider the state-dependent delay differential equation (SDDE) obtained by adding delayed perturbation to a one-dimensional ODE with a degenerate equilibrium. We prove the existence of the response solution of the equation, i.e., the quasi-periodic solution with the same frequency as the forcing. The novelty of our paper is to provide a concrete example to discuss the smoothness issues of SDDE, especially showing the analyticity of quasi-periodic solutions in some probability sense.
期刊介绍：
Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
