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Página principal > Artículos > Artículos publicados > Existence of at most two limit cycles for some non-autonomous differential equations |
Fecha: | 2023 |
Resumen: | It is know that the non-autonomous differential equations dx/dt = a(t) + b(t)|x|, where a(t) and b(t) are 1-periodic maps of class C1, have no upper bound for their number of limit cycles (isolated solutions satisfying x(0) = x(1)). We prove that if either a(t) or b(t) does not change sign, then their maximum number of limit cycles is two, taking into account their multiplicities, and that this upper bound is sharp. We also study all possible configurations of limit cycles. Our result is similar to other ones known for Abel type periodic differential equations although the proofs are quite different. |
Ayudas: | Agencia Estatal de Investigación PID2019-104658GB-I00 Agencia Estatal de Investigación CEX2020-001084-M Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Non-autonomous differential equation ; Limit cycle ; Periodic orbit |
Publicado en: | Communications on Pure and Applied Analysis, Vol. 22, Issue 3 (March 2023) , p. 970-982, ISSN 1534-0392 |
Postprint 13 p, 370.0 KB |