A new Chebyshev family with applications to Abel equations

Armengol Gasull; Chengzhi Li; Joan Torregrosa

doi:https://doi.org/10.1016/j.jde.2011.06.010

A new Chebyshev family with applications to Abel equations

Armengol Gasull, Chengzhi Li, Joan Torregrosa

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

12 Citations (Scopus)

Abstract

We prove that a family of functions defined through some definite integrals forms an extended complete Chebyshev system. The key point of our proof consists of reducing the study of certain Wronskians to the Gram determinants of a suitable set of new functions. Our result is then applied to give upper bounds for the number of isolated periodic solutions of some perturbed Abel equations. © 2011 Elsevier Inc.

Original language	English
Pages (from-to)	1635-1641
Journal	Journal of Differential Equations
Volume	252
Issue number	2
DOIs	https://doi.org/10.1016/j.jde.2011.06.010
Publication status	Published - 15 Jan 2012

Keywords

Abel equation
Chebyshev system
Integral Gram determinant
Number of zeroes of real analytic functions
Periodic solution
Primary
Secondary
Wronskian

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KW - Abel equation

KW - Chebyshev system

KW - Integral Gram determinant

KW - Number of zeroes of real analytic functions

KW - Periodic solution

KW - Primary

KW - Secondary

KW - Wronskian

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