dc.contributor.author
Álvarez, M.J.
dc.contributor.author
Gasull, A.
dc.contributor.author
Prohens, R.
dc.date.accessioned
2023-03-29T07:47:06Z
dc.date.accessioned
2024-09-19T14:25:45Z
dc.date.available
2023-03-29T07:47:06Z
dc.date.available
2024-09-19T14:25:45Z
dc.date.issued
2023-02-01
dc.identifier.uri
http://hdl.handle.net/2072/532584
dc.description.abstract
We prove that any complex differential equation with two monomials of the form z˙=azkz¯l+bzmz¯n, with k,l,m,n non-negative integers and a,b∈C, has one limit cycle at most. Moreover, we characterise when such a limit cycle exists and prove that then it is hyperbolic. For an arbitrary equation of the above form, we also solve the centre-focus problem and examine the number, position, and type of its critical points. In particular, we prove a Berlinskiĭ-type result regarding the geometrical distribution of the critical points stabilities. © 2022 The Author(s)
eng
dc.description.sponsorship
Generalitat de Catalunya; Federación Española de Enfermedades Raras, FEDER; Agència de Gestió d'Ajuts Universitaris i de Recerca, AGAUR; Agencia Estatal de Investigación, AEI: 2017-SGR-1617, CEX2020-001084-M, PID2019-104658GB-I00
dc.format.extent
16 p.
cat
dc.publisher
Elsevier
cat
dc.relation.ispartof
Journal of Mathematical Analysis and Applications
cat
dc.rights
L'accés als continguts d'aquest document queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.source
RECERCAT (Dipòsit de la Recerca de Catalunya)
dc.subject.other
Centre-focus problem; Polynomial differential equation; Uniqueness of limit cycles
cat
dc.title
Uniqueness of the limit cycles for complex differential equations with two monomials
cat
dc.type
info:eu-repo/semantics/article
cat
dc.type
info:eu-repo/semantics/publishedVersion
cat
dc.identifier.doi
10.1016/j.jmaa.2022.126663
cat
dc.rights.accessLevel
info:eu-repo/semantics/openAccess
