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 x 7¡æ x.1, and there are many results available in the literature for the first kind equ...

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Detalhes bibliográficos
Autores: Martínez-Seara Alonso, M. Teresa|||0000-0001-8421-8717, Ros Oton, Xavier|||0000-0003-1046-168X, Olm Miras, Josep Maria|||0000-0003-4925-9251
Formato: informe técnico
Fecha de publicación:2011
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/11572
Acesso em linha:https://hdl.handle.net/2117/11572
Access Level:acceso abierto
Palavra-chave:Differential equations
Abel differential equations
periodic solutions
Equacions diferencials
Àrees temàtiques de la UPC::Matemàtiques i estadística
Descrição
Resumo: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 x 7¡æ x.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