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Reid’s Construction of Minimal Principal Solution at Infinity for Linear Hamiltonian Systems

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Differential and Difference Equations with Applications (ICDDEA 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 164))

Abstract

Recently the authors introduced a theory of principal solutions at infinity for nonoscillatory linear Hamiltonian systems in the absence of the complete controllability assumption. In this theory the so-called minimal principal solution at infinity plays a distinguished role (the minimality refers to the rank of the first component of the solution). In this paper we show that the minimal principal solution at infinity can be obtained by a suitable generalization of the Reid construction of the principal solution known in the controllable case. Our new result points to some applications of the minimal principal solution at infinity, e.g., in the spectral theory of linear Hamiltonian systems.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlářská 2, CZ-61137, Brno, Czech Republic

    Peter Šepitka & Roman Šimon Hilscher

Authors
  1. Peter Šepitka
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  2. Roman Šimon Hilscher
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Corresponding author

Correspondence to Roman Šimon Hilscher .

Editor information

Editors and Affiliations

  1. Departamento de Ciências Exactas e Naturais, Academia Militar, Amadora, Portugal

    Sandra Pinelas

  2. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Zuzana Došlá

  3. Department of Mathematics and Statistics, Masaryk University, Brno, Czech Republic

    Ondřej Došlý

  4. School of Mathematics and Stastistics, Huazhong University of Science and Technology, Wuhan, China

    Peter E. Kloeden

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Šepitka, P., Hilscher, R.Š. (2016). Reid’s Construction of Minimal Principal Solution at Infinity for Linear Hamiltonian Systems. In: Pinelas, S., Došlá, Z., Došlý, O., Kloeden, P. (eds) Differential and Difference Equations with Applications. ICDDEA 2015. Springer Proceedings in Mathematics & Statistics, vol 164. Springer, Cham. https://doi.org/10.1007/978-3-319-32857-7_34

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