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Variational Approach To a Symmetric Boundary Value Problem Generated by a System of Equations and Separated Boundary Conditions
(Wiley, 2024) Ugurlu, Ekin
This work provides some information on the eigenvalues and eigenfunctions of a problem which is constructed by a system of equations and symmetric boundary conditions that includes the ordinary second-order Sturm-Liouville boundary value problem. In particular, we show that the problem has an infinite number of discrete eigenvalues with a greatest lower bound and the corresponding eigenfunctions are complete in mean and energy. We introduce the results using the variational approach that enables us to consider only continuous pair functions instead of absolutely continuous pair functions.
Citation - WoS: 1
Citation - Scopus: 1
The Spectral Analysis of a System of First-Order Equations With Dissipative Boundary Conditions
(Wiley, 2021) Ugurlu, Ekin
This paper aims to share some completeness theorems related with a boundary value problem generated by a system of equations and non-self-adjoint (dissipative) boundary conditions. Indeed, we consider a system of equations that contains a continuous analogous of the orthogonal polynomials on the unit circle. Constructing the characteristic function of the related dissipative operator, we share some completeness theorems. Moreover, we give an explicit form of the self-adjoint dilation of the dissipative operator.

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