A new Chebyshev criterion and its application to planar differential systems

2020/11/05 by Jianfeng Huang, Huang, Jianfeng, Haihua Liang +3
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Lipid metabolism and biosynthesis #Primary 34C07 #Secondary 37C05 #Tertiary 35F60

paper · pdf · doi:10.48550/arxiv.2011.02857

openalex publication_date 2020/11/05 · openalex created_date 2020/11/09 · openalex updated_date 2026/08/01

Abstract

This paper establishes a new Chebyshev criterion for some family of integrals. By virtue of this criterion we obtain several new Chebyshev families. With the help of these new families we can answer the conjecture posed by Gasull et al in 2015. %[J. Differential Equations, 258 (2015), 3286--3303]. Their applications to other two planar differential systems also show that our approach is simpler and in a unified way to handle many kinds of planar differential systems for estimating the number of limit cycles bifurcating from period annulus.

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