{"title":"重新审视扰动摆方程阿贝尔积分的零点个数","authors":"Xiuli Cen , Changjian Liu","doi":"10.1016/j.jde.2024.08.052","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we study the number of zeros of Abelian integrals associated to some perturbed pendulum equations, and derive the new lower and upper bounds for the number of zeros of these integrals. The results we obtained correct some results of Theorem B and Proposition 1.1 in the paper (Gasull et al., 2016 <span><span>[4]</span></span>).</p></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":null,"pages":null},"PeriodicalIF":2.4000,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Revisiting the number of zeros of Abelian integrals for perturbed pendulum equations\",\"authors\":\"Xiuli Cen , Changjian Liu\",\"doi\":\"10.1016/j.jde.2024.08.052\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we study the number of zeros of Abelian integrals associated to some perturbed pendulum equations, and derive the new lower and upper bounds for the number of zeros of these integrals. The results we obtained correct some results of Theorem B and Proposition 1.1 in the paper (Gasull et al., 2016 <span><span>[4]</span></span>).</p></div>\",\"PeriodicalId\":15623,\"journal\":{\"name\":\"Journal of Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022039624005345\",\"RegionNum\":2,\"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":"Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022039624005345","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
本文研究了与一些扰动摆方程相关的阿贝尔积分的零点个数，并推导出了这些积分零点个数的新下界和新上界。我们得到的结果修正了论文（Gasull 等，2016 [4]）中定理 B 和命题 1.1 的一些结果。
Revisiting the number of zeros of Abelian integrals for perturbed pendulum equations
In this paper, we study the number of zeros of Abelian integrals associated to some perturbed pendulum equations, and derive the new lower and upper bounds for the number of zeros of these integrals. The results we obtained correct some results of Theorem B and Proposition 1.1 in the paper (Gasull et al., 2016 [4]).
期刊介绍：
The Journal of Differential Equations is concerned with the theory and the application of differential equations. The articles published are addressed not only to mathematicians but also to those engineers, physicists, and other scientists for whom differential equations are valuable research tools.
Research Areas Include:
• Mathematical control theory
• Ordinary differential equations
• Partial differential equations
• Stochastic differential equations
• Topological dynamics
• Related topics
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
