Rational solutions of Abel differential equations

被引：2
|
作者：
Bravo, J. L. [1 ]
Calderon, L. A. [1 ]
Fernandez, M. [1 ]
Ojeda, I [1 ]
机构：
[1] Univ Extremadura, Dept Matemat, E-06071 Badajoz, Spain
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2022年 / 515卷 / 01期
关键词：
Periodic solution; Limit cycle; Abel equation; POLYNOMIAL SOLUTIONS; LIMIT-CYCLES; NUMBER;
D O I：
10.1016/j.jmaa.2022.126368
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the rational solutions of the Abel equation x' = A(t)x(3) + B(t)x(2) where A and B is an element of C[t]. We prove that if deg(A) is even or deg(B) > (deg(A) - 1)/2 then the equation has at most two rational solutions. For any other case, an upper bound on the number of rational solutions is obtained. Moreover, we prove that if there are more than (deg(A) + 1)/2 rational solutions then the equation admits a Darboux first integral. (C) 2022 Elsevier Inc. All rights reserved.
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页数：16
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