{"title":"On the Infinite $$\\varphi $$ -Order Solutions of Second Order Linear Differential Equations","authors":"Hui Yu, Xiaomin Li","doi":"10.1007/s40315-024-00548-1","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we consider the second order linear differential equation </p><p> where <i>A</i>, <i>B</i> and <i>F</i> with <span>\\(B\\not \\equiv 0\\)</span> are entire functions. We find some appropriate conditions on <i>A</i>, <i>B</i> and <i>F</i> in terms of the <span>\\(\\varphi \\)</span>-order which guarantee that every non-constant entire solution <i>f</i> of (†) has infinite <span>\\(\\varphi \\)</span>-order, along with an additional relation between the hyper-<span>\\(\\varphi \\)</span>-order of <i>f</i> and the <span>\\(\\varphi \\)</span>-order of the dominating coefficient in (†).</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods and Function Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40315-024-00548-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider the second order linear differential equation
where A, B and F with \(B\not \equiv 0\) are entire functions. We find some appropriate conditions on A, B and F in terms of the \(\varphi \)-order which guarantee that every non-constant entire solution f of (†) has infinite \(\varphi \)-order, along with an additional relation between the hyper-\(\varphi \)-order of f and the \(\varphi \)-order of the dominating coefficient in (†).
期刊介绍：
CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.
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