Rational solutions and limit cycles of polynomial and trigonometric Abel equations
We study the Abel differential equation x ′ = A(t)x 3 + B(t)x 2 + C(t)x. Specifically, we find bounds on the number of its rational solutions when A(t), B(t) and C(t) are polynomials with real or complex coefficients; and on the number of rational limit cycles when A(t), B(t) and C(t) are trigonomet...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2025
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Abel-egyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2025.1.18 |
| Online Access: | http://acta.bibl.u-szeged.hu/88898 |
| Tartalmi kivonat: | We study the Abel differential equation x ′ = A(t)x 3 + B(t)x 2 + C(t)x. Specifically, we find bounds on the number of its rational solutions when A(t), B(t) and C(t) are polynomials with real or complex coefficients; and on the number of rational limit cycles when A(t), B(t) and C(t) are trigonometric polynomials with real coefficients. |
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| Terjedelem/Fizikai jellemzők: | 16 |
| ISSN: | 1417-3875 |