Periodic solutions with nonconstant sign in Abel equations of the second kind
The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation xmaps tox−1, and there are many results available in the literature for the first kind e...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/12584 |
| Acceso en línea: | https://hdl.handle.net/2117/12584 https://dx.doi.org/10.1016/j.jmaa.2011.02.084 |
| Access Level: | acceso abierto |
| Palabra clave: | Equations, Abelian Abel differential equations Periodic solutions Equacions Classificació AMS::14 Algebraic geometry::14K Abelian varieties and schemes Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals |
| Sumario: | The study of periodic solutions with constant sign in the Abel equation of the second kind can be made through the equation of the first kind. This is because the situation is equivalent under the transformation xmaps tox−1, and there are many results available in the literature for the first kind equation. However, the equivalence breaks down when one seeks for solutions with nonconstant sign. This note is devoted to periodic solutions with nonconstant sign in Abel equations of the second kind. Specifically, we obtain sufficient conditions to ensure the existence of a periodic solution that shares the zeros of the leading coefficient of the Abel equation. Uniqueness and stability features of such solutions are also studied. |
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