Non-limit-circle and limit-point criteria for symplectic and linear Hamiltonian systems

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Year of publication 2023
Type Article in Periodical
Magazine / Source Mathematische Nachrichten
MU Faculty or unit

Faculty of Science

Keywords criteria; limit-circle case; limit-point case; linear Hamiltonian differential system; square-integrable solution; symplectic system; time scale
Description Several necessary and/or sufficient conditions for the existence of a non–square-integrable solution of symplectic dynamic systems with general linear dependence on the spectral parameter on time scales are established and a sufficient condition for the limit-point case is derived. Almost all presented results are new even in the continuous and discrete cases, that is, for the linear Hamiltonian differential systems and for the discrete symplectic systems, respectively.
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