A new Chebyshev family with applications to Abel equations

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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. © 2011 Elsevier Inc.
Original languageEnglish
Pages (from-to)1635-1641
JournalJournal of Differential Equations
Volume252
Issue number2
DOIs
Publication statusPublished - 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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