A Chebyshev criterion with applications
A. Gasull (Universitat Autònoma de Barcelona)
A. Geyer (TU Delft - Electrical Engineering, Mathematics and Computer Science)
F. Mañosas (Universitat Autònoma de Barcelona)
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Abstract
We show that a family of certain definite integrals forms a Chebyshev system if two families of associated functions appearing in their integrands are Chebyshev systems as well. We apply this criterion to several examples which appear in the context of perturbations of periodic non-autonomous ODEs to determine bounds on the number of isolated periodic solutions, as well as to persistence problems of periodic solutions for perturbed Hamiltonian systems.
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