Uniqueness of the limit cycles for complex differential equations with two monomials

Gasull, A.; Álvarez, M.J.; Prohens, R.

dc.contributor.author	Gasull, A.
dc.contributor.author	Álvarez, M.J.
dc.contributor.author	Prohens, R.
dc.date.accessioned	2023-08-02T06:56:32Z
dc.identifier.uri	http://hdl.handle.net/11201/161404
dc.description.abstract	[eng] We prove that any complex differential equation with two monomials of the form, with non-negative integers and, 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.
dc.format	application/pdf
dc.relation.isformatof	Versió postprint del document publicat a: https://doi.org/10.1016/j.jmaa.2022.126663
dc.relation.ispartof	Journal of Mathematical Analysis and Applications, 2023, vol. 518, num. 1, p. 1-16
dc.subject.classification	51 - Matemàtiques
dc.subject.classification	004 - Informàtica
dc.subject.other	51 - Mathematics
dc.subject.other	004 - Computer Science and Technology. Computing. Data processing
dc.title	Uniqueness of the limit cycles for complex differential equations with two monomials
dc.type	info:eu-repo/semantics/article
dc.type	info:eu-repo/semantics/acceptedVersion
dc.date.updated	2023-08-02T06:56:33Z
dc.date.embargoEndDate	info:eu-repo/date/embargoEnd/2100-01-01
dc.embargo	2100-01-01
dc.subject.keywords	polynomial differential equation
dc.subject.keywords	Uniqueness of limit cycles
dc.subject.keywords	Centre-focus problem
dc.rights.accessRights	info:eu-repo/semantics/embargoedAccess
dc.identifier.doi	https://doi.org/10.1016/j.jmaa.2022.126663