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Antiprincipal solutions at infinity for symplectic systems on time scales

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DŘÍMALOVÁ Iva ŠIMON HILSCHER Roman

Rok publikování 2020
Druh Článek v odborném periodiku
Časopis / Zdroj Electronic Journal of Qualitative Theory of Differential Equations
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Citace
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Doi http://dx.doi.org/10.14232/ejqtde.2020.1.44
Klíčová slova Symplectic system on time scale; Antiprincipal solution at infinity; Principal solution at infinity; Nonoscillation; Linear Hamiltonian system; Normality
Popis In this paper we introduce a new concept of antiprincipal solutions at infinity for symplectic systems on time scales. This concept complements the earlier notion of principal solutions at infinity for these systems by the second author and Sepitka (2016). We derive main properties of antiprincipal solutions at infinity, including their existence for all ranks in a given range and a construction from a certain minimal antiprincipal solution at infinity. We apply our new theory of antiprincipal solutions at infinity in the study of principal solutions, and in particular in the Reid construction of the minimal principal solution at infinity. In this work we do not assume any normality condition on the system, and we unify and extend to arbitrary time scales the theory of antiprincipal solutions at infinity of linear Hamiltonian differential systems and the theory of dominant solutions at infinity of symplectic difference systems.
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