Proof of Artes-Llibre-Valls's conjectures for the Higgins-Selkov and the Selkov systems

Release time:2019-07-11

Journal:JOURNAL OF DIFFERENTIAL EQUATIONS

Place of Publication:ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA

Key Words:Limit cycle; Higgins-Selkov system; Selkov system; Lienard system

Abstract:The aim of this paper is to prove Artes-Llibre-Valls's conjectures on the uniqueness of limit cycles for the Higgins-Selkov system and the Selkov system. In order to apply the limit cycle theory for Lienard systems, we change the Higgins-Selkov and the Selkov systems into Lienard systems first. Then, we present two theorems on the nonexistence of limit cycles of Lienard systems. At last, the conjectures can be proven by these theorems and some techniques applied for Lienard systems.

First Author:Chen Hebai

Indexed by:Unit Twenty Basic Research

Correspondence Author:Tang Yilei

Document Code:10.1016/j.jde.2018.12.011

Discipline:数学

Document Type:J

Volume:266

Issue:11

Page Number:7638-7657

ISSN No.:0022-0396

Translation or Not:no

Date of Publication:2019-05-19