{"title":"某些类型二项式微分方程的全解","authors":"Shuang-Shuang Yang, Liang-Wen Liao, Xiao-Qing Lu","doi":"10.1007/s40315-024-00556-1","DOIUrl":null,"url":null,"abstract":"<p>Inspired by the questions Gundersen and Yang proposed, we investigate the exact forms of the entire solutions of the following two types of binomial differential equations </p><span>$$\\begin{aligned} a(z)ff''+b(z)(f')^2=c(z)e^{2q(z)}; \\\\ a(z)f'f''+b(z)f^2=c(z)e^{2q(z)}, \\end{aligned}$$</span><p>where <i>a</i>, <i>b</i>, <i>c</i> are polynomials with no common zeros satisfying <span>\\(abc\\not \\equiv 0\\)</span>, and <i>q</i> is a non-constant polynomial.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"22 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Entire Solutions of Certain Type Binomial Differential Equations\",\"authors\":\"Shuang-Shuang Yang, Liang-Wen Liao, Xiao-Qing Lu\",\"doi\":\"10.1007/s40315-024-00556-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Inspired by the questions Gundersen and Yang proposed, we investigate the exact forms of the entire solutions of the following two types of binomial differential equations </p><span>$$\\\\begin{aligned} a(z)ff''+b(z)(f')^2=c(z)e^{2q(z)}; \\\\\\\\ a(z)f'f''+b(z)f^2=c(z)e^{2q(z)}, \\\\end{aligned}$$</span><p>where <i>a</i>, <i>b</i>, <i>c</i> are polynomials with no common zeros satisfying <span>\\\\(abc\\\\not \\\\equiv 0\\\\)</span>, and <i>q</i> is a non-constant polynomial.</p>\",\"PeriodicalId\":49088,\"journal\":{\"name\":\"Computational Methods and Function Theory\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-08-09\",\"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/s40315-024-00556-1\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods and Function Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40315-024-00556-1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Entire Solutions of Certain Type Binomial Differential Equations
Inspired by the questions Gundersen and Yang proposed, we investigate the exact forms of the entire solutions of the following two types of binomial differential equations
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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