{"title":"二阶保守方程的最大周期环数","authors":"A. Gritsans, Inara Yermachenko","doi":"10.3846/mma.2021.13979","DOIUrl":null,"url":null,"abstract":"We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.","PeriodicalId":49861,"journal":{"name":"Mathematical Modelling and Analysis","volume":"114 1","pages":"612-630"},"PeriodicalIF":1.6000,"publicationDate":"2021-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the Maximum number of period annuli for second order conservative equations\",\"authors\":\"A. Gritsans, Inara Yermachenko\",\"doi\":\"10.3846/mma.2021.13979\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.\",\"PeriodicalId\":49861,\"journal\":{\"name\":\"Mathematical Modelling and Analysis\",\"volume\":\"114 1\",\"pages\":\"612-630\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2021-11-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modelling and Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3846/mma.2021.13979\",\"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":"Mathematical Modelling and Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3846/mma.2021.13979","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Maximum number of period annuli for second order conservative equations
We consider a second order scalar conservative differential equation whose potential function is a Morse function with a finite number of critical points and is unbounded at infinity. We give an upper bound for the number of nonglobal nontrivial period annuli of the equation and prove that the upper bound obtained is sharp. We use tree theory in our considerations.
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