Yeni Tipten Sturm-Liouville Problemlerinin Ürettiği Diferansiyel Operatörlerin Kendine Eşlenikliği ve Pozitivliği

Olğar, Hayati

doi:10.17776/csj.451174

Cited by 2 publications

(1 citation statement)

References 31 publications

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“…Recently, there has been an increasing interest in Sturm-Liouville boundary value problems defined on two or more disjoint segments with common ends, the so-called many-interval SLPs (see, for example, [9][10][11][12][13][14][15][16][17][18][19][20][21] and references cited therein). To deal with such multi-interval boundary value problems, naturally, additional conditions (the so-called transmission conditions, jump conditions, interface conditions, and impulsive conditions) are imposed at these common endpoints.…”

Section: Introductionmentioning

confidence: 99%

Non-classical periodic boundary value problems with impulsive conditions

ÖZTÜRK

Mukhtarov

Aydemir

2023

Journal of New Results in Science

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This study investigates some spectral properties of a new type of periodic Sturm-Liouville problem. The problem under consideration differs from the classical ones in that the differential equation is given on two disjoint segments that have a common end, and two additional interaction conditions are imposed on this common end (such interaction conditions are called various names, including transmission conditions, jump conditions, interface conditions, impulsive conditions, etc.). At first, we proved that all eigenvalues are real and there is a corresponding real-valued eigenfunction for each eigenvalue. Then we showed that two eigenfunctions corresponding to different eigenvalues are orthogonal. We also defined some left and right-hand solutions, in terms of which we constructed a new transfer characteristic function. Finally, we have defined asymptotic formulas for the transfer characteristic functions and also for the eigenvalues. The results obtained are a generalization of similar results of the classical Sturm-Liouville theory.

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Section: Introductionmentioning

confidence: 99%

Non-classical periodic boundary value problems with impulsive conditions

ÖZTÜRK

Mukhtarov

Aydemir

2023

Journal of New Results in Science

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On completeness of weak eigenfunctions for multi-interval Sturm-Liouville equations with boundary-interface conditions

Olğar

2023

Demonstratio Mathematica

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The goal of this study is to analyse the eigenvalues and weak eigenfunctions of a new type of multi-interval Sturm-Liouville problem (MISLP) which differs from the standard Sturm-Liouville problems (SLPs) in that the Strum-Liouville equation is defined on a finite number of non-intersecting subintervals and the boundary conditions are set not only at the endpoints but also at finite number internal points of interaction. For the self-adjoint treatment of the considered MISLP, we introduced some self-adjoint linear operators in such a way that the considered multi-interval SLPs can be interpreted as operator-pencil equation. First, we defined a concept of weak solutions (eigenfunctions) for MISLPs with interface conditions at the common ends of the subintervals. Then, we found some important properties of eigenvalues and corresponding weak eigenfunctions. In particular, we proved that the spectrum is discrete and the system of weak eigenfunctions forms a Riesz basis in appropriate Hilbert space.

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Yeni Tipten Sturm-Liouville Problemlerinin Ürettiği Diferansiyel Operatörlerin Kendine Eşlenikliği ve Pozitivliği

Abstract: It is purpose of this paper to investigate Sturm-Liouville equation

Cited by 2 publications

References 31 publications

Non-classical periodic boundary value problems with impulsive conditions

Non-classical periodic boundary value problems with impulsive conditions

On completeness of weak eigenfunctions for multi-interval Sturm-Liouville equations with boundary-interface conditions

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