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    On a fourth order boundary value problem with periodic and transmission conditions
    (Iğdır Üniversitesi, 2025) Cabri, Olgun
    This study investigates the asymptotic expressions of eigenvalues and eigenfunctions for a fourth-order boundary value problem subject to periodic boundary conditions. It is also examined in the problem with transmission boundary conditions at zero. At t=0, one of the transmission boundary conditions have jump discontinuity. Firstly, asymptotic formulas of fundamental solutions are found. The asymptotic formulas of the eigenvalues are computed by the aid of Rouche method. Finally corresponding eigenfunctions to these eigenvalues are presented.
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    On q sturm liouville operator with periodic boundary conditions
    (Universal Wiser Publisher, 2024) Cabri, Olgun; Toprakseven, Şuayip
    In this study, we consider q-Sturm Liouville operator with periodic boundary conditions. An asymptotic expression of the solution is obtained. With the help of this asymptotic representation, an asymptotic solution of the characteristic equation is presented. An application of the Rouche theorem, asymptotic expressions of eigenvalues are obtained.
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    On the Riesz basis property of the root functions of a discontinuous boundary problem
    (Wiley, 2019) Cabri, Olgun
    In this paper, we consider the nonself-adjoint discontinuous Sturm Liouvilleoperator with periodic (antiperiodic) boundary condition and compatibility con-ditions. Asymptotic formulas of eigenvalues and eigenfunctions of the operatorare obtained. Using these accurate asymptotic formulas for eigenvalues andeigenfunctions, we prove the basisness of the root functions of the boundaryvalue problem.
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    On the riesz basisness of root functions of a sturm–liouville operator with conjugate conditions
    (Maik Nauka/Interperiodica/Springer, 2020) Cabri, Olgun; Mamedov, K. R.
    This paper aims to prove the Riesz basisness of root functions of the non-selfadjoint a discontinuous Sturm-Liouville operator with periodic boundary condition which are not strong regular and with conjugate conditions. It is assumed that the potentials of differential operator are complex valued and continuously differentiable functions and both conjugate conditions have different finite one-sided limits at point zero. In order to prove Riesz basisness of root functions, we firstly acquire asymptotic expressions of fundamental solutions. By using these solutions in the characteristic determinant, it is obtained asymptotic formulas of eigenvalues by means of Rouche theorem. Then by the aid of asymptotic formulas of eigenfunctions,Riesz basisness is shown. it is also proved the Riesz basisness of root functions of the same operator with antiperiodic boundary conditions and with same conjugate conditions.
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    Riesz basisness of root functions of a sturm–liouville operator with conjugate conditions
    (Pleiades Publishing, 2020) Cabri, Olgun; Mamedov, Kr Residoglu
    In this paper we are interested in Riesz basisness of root functions of the non-selfadjoint a discontinuous Sturm–Liouville operator with periodic boundary condition which are not strong regular and with conjugate conditions. Here we assume that the potentials are complex valued and continuously differentiable functions. One of conjugate conditions have different finite one-sided limits at point zero. In order to prove Riesz basisness of root functions, we firstly obtain asymptotic expressions of fundamental solutions. Putting these solutions into characteristic determinant, we get asymptotic formulas of eigenvalues by means of Rouche theorem. Asymptotic formulas of eigenfunctions acquired by obtained relation and fundamental solutions. By the aid of asymptotic formulas of eigenfunctions and Bessel properties of eigenfunctions we prove the basisness of the root functions of the boundary value problem. We also prove the Riesz basisness of root functions of the same operator with antiperiodic boundary conditions and with same conjugate conditions.