تقرير
Rational Solutions of Abel Differential Equations
| العنوان: | Rational Solutions of Abel Differential Equations |
|---|---|
| المؤلفون: | Bravo, J. L., Calderon, L. A., Fernandez, M., Ojeda, I. |
| سنة النشر: | 2021 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Classical Analysis and ODEs |
| الوصف: | We study the rational solutions of the Abel equation $x'=A(t)x^3+B(t)x^2$ where $A,B\in C[t]$. 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. Comment: 19 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2109.07853 |
| رقم الأكسشن: | edsarx.2109.07853 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |