{"title":"The Mathieu Equation near the Boundaries of the Second and Third Resonance Zones","authors":"V. M. Budanov, L. F. Davudova","doi":"10.3103/S0027133021060030","DOIUrl":null,"url":null,"abstract":"<p>A second-order differential equation with periodic coefficients is considered. The reduction of this equation to a first-order nonlinear equation is shown. The fourth approximation of the second resonance zone and the third approximation of the third resonance zone are constructed for the Mathieu equation describing the behavior of solutions near the boundaries of these zones.</p>","PeriodicalId":710,"journal":{"name":"Moscow University Mechanics Bulletin","volume":"76 6","pages":"147 - 155"},"PeriodicalIF":0.3000,"publicationDate":"2022-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mechanics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.3103/S0027133021060030","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
A second-order differential equation with periodic coefficients is considered. The reduction of this equation to a first-order nonlinear equation is shown. The fourth approximation of the second resonance zone and the third approximation of the third resonance zone are constructed for the Mathieu equation describing the behavior of solutions near the boundaries of these zones.
期刊介绍：
Moscow University Mechanics Bulletin is the journal of scientific publications, reflecting the most important areas of mechanics at Lomonosov Moscow State University. The journal is dedicated to research in theoretical mechanics, applied mechanics and motion control, hydrodynamics, aeromechanics, gas and wave dynamics, theory of elasticity, theory of elasticity and mechanics of composites.
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