Limit cycles for generalized Abel equations
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...
| Autores: | , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2005 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/944 |
| Acesso em linha: | https://hdl.handle.net/2117/944 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Differential equations Differentiable dynamical systems Abel equation limit cycles planar differential equations Equacions diferencials ordinàries Sistemes dinàmics diferenciables Classificació AMS::34 Ordinary differential equations::34C Qualitative theory Classificació AMS::37 Dynamical systems and ergodic theory::37C Smooth dynamical systems: general theory |
| Resumo: | 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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