ON THE NUMBER OF NONTRIVIAL RATIONAL SOLUTIONS FOR ABEL EQUATIONS

被引：0
|
作者：
Qian, Xinjie [1 ]
Yang, Jiazhong [2 ]
机构：
[1] Jinling Inst Technol, Coll Sci, Nanjing 211169, Peoples R China
[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China
来源：
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION | 2022年 / 12卷 / 06期
基金：
美国国家科学基金会;
关键词：
Abel differential equations; nontrivial rational solution; Lienard system; rational invariant curve; POLYNOMIAL SOLUTIONS; LIMIT-CYCLES;
D O I：
10.11948/20220061
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, a systematic algorithm is provided to determine the sharp upper bound on the number of nontrivial rational solutions for the Abel differential equations dy/dx = f(m) (x) y(2) + g(n) (x)y(3) , where f(m) (x) and g(n) (x) are real polynomials of degree m and n respectively. As an application, we present a thorough study for an important case, (m, n) = (4, 9).
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页码：2541 / 2554
页数：14
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