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Citation - WoS: 3
Citation - Scopus: 3
A New Insight To the Hamiltonian Systems With a Finite Number of Spectral Parameters
(Taylor & Francis Ltd, 2023) Ugurlu, Ekin
In 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.
Citation - WoS: 2
Citation - Scopus: 3
Investigation of the Eigenvalues and Root Functions of the Boundary Value Problem Together With a Transmission Matrix
(Taylor & Francis Ltd, 2020) Ugurlu, Ekin
In this paper, we consider a singular even-order Hamiltonian system on the union of two intervals together with appropriate boundary and transmission conditions. For investigating the spectral properties of the problem we pass to the inverse operator with an explicit form and we prove some completeness theorems.

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