{"title":"On the Solvability of a Periodic Problem for a System of Second-Order Nonlinear Ordinary Differential Equations","authors":"E. Mukhamadiev, A. N. Naimov","doi":"10.1134/s0012266124030030","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The solvability of a periodic problem for a system of nonlinear second-order ordinary\ndifferential equations with a positively homogeneous main part is investigated. New conditions are\nfound that ensure an a priori estimate for the solutions of the periodic problem under\nconsideration. The conditions are stated in terms of the properties of the positively homogeneous\nmain part of the system. Under the a priori estimate, using and developing methods for calculating\nthe mapping degree for vector fields, we prove a theorem on the solvability of the periodic problem\nthat generalizes the results previously obtained by the present authors on the study of the periodic\nproblem for systems of second-order nonlinear ordinary differential equations.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124030030","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The solvability of a periodic problem for a system of nonlinear second-order ordinary
differential equations with a positively homogeneous main part is investigated. New conditions are
found that ensure an a priori estimate for the solutions of the periodic problem under
consideration. The conditions are stated in terms of the properties of the positively homogeneous
main part of the system. Under the a priori estimate, using and developing methods for calculating
the mapping degree for vector fields, we prove a theorem on the solvability of the periodic problem
that generalizes the results previously obtained by the present authors on the study of the periodic
problem for systems of second-order nonlinear ordinary differential equations.
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