Publication details

On square integrable solutions and principal and antiprincipal solutions for linear Hamiltonian systems

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Authors

ŠIMON HILSCHER Roman ZEMÁNEK Petr

Year of publication 2018
Type Article in Periodical
Magazine / Source Annali di Matematica Pura ed Applicata. Series IV
MU Faculty or unit

Faculty of Science

Citation
Web http://dx.doi.org/10.1007/s10231-017-0679-7
Doi http://dx.doi.org/10.1007/s10231-017-0679-7
Field General mathematics
Keywords Linear Hamiltonian system; square integrable solution; Weyl solution; minimal principal solution at infinity; antiprincipal solution at infinity; limit point case; limit circle case
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Description New results in the Weyl-Titchmarsh theory for linear Hamiltonian differential systems are derived by using principal and antiprincipal solutions at infinity. In particular, a non-limit circle case criterion is established and a close connection between the Weyl solution and the minimal principal solution at infinity is shown in the limit point case. In addition, the square integrability of the columns of the minimal principal solution at infinity is investigated. All results are obtained without any controllability assumption. Several illustrative examples are also provided.
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