Existence of at most two limit cycles for some non-autonomous differential equations
Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Zhao, Yulin (Sun Yat-sen University. School of Mathematics)

Data:	2023
Resum:	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.
Ajuts:	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
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Non-autonomous differential equation ; Limit cycle ; Periodic orbit
Publicat a:	Communications on Pure and Applied Analysis, Vol. 22, Issue 3 (March 2023) , p. 970-982, ISSN 1534-0392

DOI: 10.3934/cpaa.2023016

Postprint 13 p, 370.0 KB

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