On the rational limit cycles of Abel equations

2018 ◽  
Vol 110 ◽  
pp. 28-32 ◽  
Author(s):  
Changjian Liu ◽  
Chunhui Li ◽  
Xishun Wang ◽  
Junqiao Wu
Keyword(s):  
Limit Cycles ◽  
Abel Equations

Characterization of the Existence of Non-trivial Limit Cycles for Generalized Abel Equations

2021 ◽  
Vol 20 (1) ◽  
Author(s):  
M. J. Álvarez ◽  
J. L. Bravo ◽  
M. Fernández ◽  
R. Prohens
Keyword(s):  
Limit Cycles ◽  
Abel Equations

Alien limit cycles in Abel equations

2020 ◽  
Vol 482 (1) ◽  
pp. 123525 ◽  
Author(s):  
M.J. Álvarez ◽  
J.L. Bravo ◽  
M. Fernández ◽  
R. Prohens
Keyword(s):  
Limit Cycles ◽  
Abel Equations

scholarly journals On the Number of Limit Cycles in Generalized Abel Equations

2020 ◽  
Vol 19 (4) ◽  
pp. 2343-2370
Author(s):  
Jianfeng Huang ◽  
Joan Torregrosa ◽  
Jordi Villadelprat
Keyword(s):  
Limit Cycles ◽  
Abel Equations

scholarly journals Centers and limit cycles for a family of Abel equations

2017 ◽  
Vol 453 (1) ◽  
pp. 485-501 ◽  
Author(s):  
M.J. Álvarez ◽  
J.L. Bravo ◽  
M. Fernández ◽  
R. Prohens
Keyword(s):  
Limit Cycles ◽  
Abel Equations

scholarly journals Limit cycles of Abel equations of the first kind

2015 ◽  
Vol 423 (1) ◽  
pp. 734-745 ◽  
Author(s):  
A. Álvarez ◽  
J.L. Bravo ◽  
M. Fernández
Keyword(s):  
Limit Cycles ◽  
Abel Equations

Iterative approximation of limit cycles for a class of Abel equations

2008 ◽  
Vol 237 (23) ◽  
pp. 3159-3164 ◽  
Author(s):  
Enric Fossas ◽  
Josep M. Olm ◽  
Hebertt Sira-Ramírez
Keyword(s):  
Limit Cycles ◽  
Iterative Approximation ◽  
Abel Equations

scholarly journals Rational Limit Cycles on Abel Polynomial Equations

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 885 ◽  
Author(s):  
Claudia Valls
Keyword(s):  
Limit Cycles ◽  
Upper Bounds ◽  
Polynomial Equations ◽  
Abel Polynomial ◽  
Real Polynomials ◽  
Abel Equations

In this paper we deal with Abel equations of the form d y / d x = A 1 ( x ) y + A 2 ( x ) y 2 + A 3 ( x ) y 3 , where A 1 ( x ) , A 2 ( x ) and A 3 ( x ) are real polynomials and A 3 ≢ 0 . We prove that these Abel equations can have at most two rational (non-polynomial) limit cycles when A 1 ≢ 0 and three rational (non-polynomial) limit cycles when A 1 ≡ 0 . Moreover, we show that these upper bounds are sharp. We show that the general Abel equations can always be reduced to this one.

scholarly journals Existence of non-trivial limit cycles in Abel equations with symmetries

2013 ◽  
Vol 84 ◽  
pp. 18-28 ◽  
Author(s):  
M.J. Álvarez ◽  
J.L. Bravo ◽  
M. Fernández
Keyword(s):  
Limit Cycles ◽  
Abel Equations

scholarly journals The number of limit cycles for generalized Abel equations with periodic coefficients of definite sign

2009 ◽  
Vol 8 (5) ◽  
pp. 1493-1501 ◽  
Author(s):  
Amelia Álvarez ◽  
◽  
José-Luis Bravo ◽  
Manuel Fernández
Keyword(s):  
Limit Cycles ◽  
Periodic Coefficients ◽  
Abel Equations
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