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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. (C) 2018 Elsevier Inc. All rights reserved.
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JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN: 0022-0396
Year: 2019
Issue: 11
Volume: 266
Page: 7638-7657
2 . 1 9 2
JCR@2019
2 . 4 0 0
JCR@2023
ESI Discipline: MATHEMATICS;
ESI HC Threshold:59
JCR Journal Grade:1
CAS Journal Grade:1
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