Limit cycles for generalized Abel equations
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hdl:2117/944
Tipus de documentArticle
Data publicació2005
Condicions d'accésAccés obert
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Abstract
This paper deals with the problem of finding upper bounds on the number
of periodic solutions of a class of one-dimensional non-autonomous differential
equations: those with the right-hand sides being polynomials of degree n and
whose coeficients are real smooth 1-periodic functions. The case n = 3 gives
the so-called Abel equations which have been thoroughly studied and are quite
understood. We consider two natural generalizations of Abel equations. Our
results extend previous works of Lins Neto and Panov and try to step forward
in the understanding of the case n > 3. They can be applied, as well, to control
the number of limit cycles of some planar ordinary differential equations.
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050602guillamon.pdf | 208,9Kb | Visualitza/Obre |