Ugurlu, Ekin2023-11-222025-09-182023-11-222025-09-182023Ekin, Uğurlu. (2023). "A new insight to the Hamiltonian systems with a finite number of spectral parameters", Quaestiones Mathematicae, Vol.46, No. 5, pp. 887-908.1607-36061727-933Xhttps://doi.org/10.2989/16073606.2022.2045643https://hdl.handle.net/20.500.12416/13692In this article, we introduce a new first-order differential equation containing a finite number of spectral parameters and some results on the solutions of this equation. In particular, with the aid of the nested-circles approach we share a lower bound for the number of linearly independent square-integrable solutions of the equation. We share some limit-point criterias. Moreover, we show that some known and unknown scalar and matrix differential equations can be embedded into this new first-order equation. Using the obtained results we present some additional results for some system of scalar multiparameter differential equations. Finally, we share some relations between the characteristic function of a regular boundary-value problem and the kernel of related integral operator.eninfo:eu-repo/semantics/closedAccessPrimarySecondaryFirst-Order SystemWeyl'S TheoryMultiparameter Eigenvalue ProblemArticle10.2989/16073606.2022.20456432-s2.0-85128077810