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| 摘要: |
| 本文研究了二阶Fermat型常微分方程(a1f+b1f′+c1f′′)2+(a2f+b2f′+c2f′′)2=γ的整函数解的问题,其中γ是C上的整函数. 利用Nevanlinna值分布理论的方法,获得了方程存在整函数解的充要条件, 并且给出了解的表达形式. |
| 关键词: 二阶Fermat型复微分方程 Nevanlinna值分布理论 整函数 |
| DOI： |
| 分类号:O175.29 |
| 基金项目:国家自然科学基金资助(11701006);安徽省高等学校科学研究项目资助(2022AH050329, 2022AH050290). |
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| ON ENTIRE SOLUTIONS OF THE SECOND-ORDER FERMAT-TYPE ORDINARY DIFFERENTIAL EQUATIONS |
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ZHANG Yu,YANG Liu
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| Abstract: |
| This article investigates the problem of the entire function solution of second-order Fermat type ordinary difierential equation (a1f+b1f′+c1f′′)2+(a2f+b2f′+c2f′′)2=γ, where γ is the entire function on C. Using the method of Nevanlinna value distribution theory, we obtain the necessary and sufficient conditions for the existence of an entire function solution to the equation, and provide the expression of the solution. |
| Key words: second-order Fermat-type ordinary difierential equation Nevanlinna value distribution theory entire function |
