{"title":"Monotonicity of the period map for the equation $$-\\varphi ''+\\varphi -\\varphi ^{k}=0$$","authors":"Giovana Alves, Fábio Natali","doi":"10.1007/s00605-024-01969-9","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we establish the monotonicity of the period map in terms of the energy levels for certain periodic solutions of the equation <span>\\(-\\varphi ''+\\varphi -\\varphi ^{k}=0\\)</span>, where <span>\\(k>1\\)</span> is a real number. We present a new approach to demonstrate this property, utilizing spectral information of the corresponding linearized operator around the periodic solution and tools related to Floquet theory.</p>","PeriodicalId":18913,"journal":{"name":"Monatshefte für Mathematik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Monatshefte für Mathematik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00605-024-01969-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
In this paper, we establish the monotonicity of the period map in terms of the energy levels for certain periodic solutions of the equation \(-\varphi ''+\varphi -\varphi ^{k}=0\), where \(k>1\) is a real number. We present a new approach to demonstrate this property, utilizing spectral information of the corresponding linearized operator around the periodic solution and tools related to Floquet theory.
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