{"title":"构建非线性微分方程周期解的方法","authors":"V. M. Budanov","doi":"10.1134/s0012266124050021","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We justify an analytical method for constructing periodic solutions of nonlinear systems of\nordinary differential equations of polynomial type. Periodic solutions are constructed in the form\nof Fourier series in which the coefficients are polynomials depending on a parameter, which is not\nassumed to be small. Two examples are considered: the van der Pol equation and the Lorenz\nsystem.\n</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"9 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Method for Constructing Periodic Solutions of Nonlinear Differential Equations\",\"authors\":\"V. M. Budanov\",\"doi\":\"10.1134/s0012266124050021\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> We justify an analytical method for constructing periodic solutions of nonlinear systems of\\nordinary differential equations of polynomial type. Periodic solutions are constructed in the form\\nof Fourier series in which the coefficients are polynomials depending on a parameter, which is not\\nassumed to be small. Two examples are considered: the van der Pol equation and the Lorenz\\nsystem.\\n</p>\",\"PeriodicalId\":50580,\"journal\":{\"name\":\"Differential Equations\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-09-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266124050021\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124050021","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Method for Constructing Periodic Solutions of Nonlinear Differential Equations
Abstract
We justify an analytical method for constructing periodic solutions of nonlinear systems of
ordinary differential equations of polynomial type. Periodic solutions are constructed in the form
of Fourier series in which the coefficients are polynomials depending on a parameter, which is not
assumed to be small. Two examples are considered: the van der Pol equation and the Lorenz
system.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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