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

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13 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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https://ddd.uab.cat/record/150548

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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. {\textcopyright} 2011 Elsevier Inc.",

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T1 - A new Chebyshev family with applications to Abel equations

AU - Gasull, Armengol

AU - Li, Chengzhi

AU - Torregrosa, Joan

PY - 2012/1/15

Y1 - 2012/1/15

N2 - 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.

AB - 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.

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

U2 - https://doi.org/10.1016/j.jde.2011.06.010

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

M3 - Article

VL - 252

SP - 1635

EP - 1641

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 2

ER -

A new Chebyshev family with applications to Abel equations

Abstract

Keywords

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