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).

引用

页码：2541 / 2554

页数：14

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