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STURM-LIoUVILLE PRoBLEMS WITH EIGENDEPENDENT BoUNDARY AND TRANSMISSIoNS CoNDITIoNS

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Acta Mathematica Scientia 2005年第4期25卷 731-740页

作者： Z.Akdog■an M.Demirci o.sh.mukhtarov Department of Mathematics Faculty of Science-Art Gaziosmanpas■a University 60100 Tokat TurkeyDepartment of Mathematics Faculty of Science-Art Gaziosmanpas■a University 60100 Tokat TurkeyDepartment of Mathematics Faculty of Science-Art Gaziosmanpas■a University 60100 Tokat Turkey

The purpose of this paper is to extend some fundamental spectral properties of regular Sturm-Liouville problems to special kind discontinuous boundary value problem, which consist of a Sturm-Liouville equation with piecewise continuous potential together with eigenvalue parameter on the boundary and transmission conditions. The authors suggest their own approach for finding asymptotic approximations formulas for eigenvalues and eigenfunctions of such discontinuous problems.

关键词： Sturm-Liouville problems transmission conditions asymptotic of eigenvalues and eigenfunctions discontinuous boundary-value problems

ASYMPToTIC BEHAVIoUR oF EIGENVALUES FoR THE DISCoNTINUoUS BoUNDARY-VALUE PRoBLEM WITH FUNCTIoNAL-TRANSMISSIoN CoNDITIoNS

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Acta Mathematica Scientia 2002年第3期22卷 335-345页

作者： o.sh.mukhtarov Department of Mathematics, Science and Arts Faculty, Gaziosmanpasa University, Tokat, TurkeyMustafa Kandemir Department of Mathematics, Faculty of A mas y a Education, ondokuz Mayis University, Amasya, Turkey Department of Mathematics Science and Arts Faculty Gaziosmanpasa University Tokat Turkey Department of Mathematics Faculty of Amasya Education Ondokuz Mayis University Amasya Turkey

In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and linear functionals is investigated. So, the problem is not pure boundary-value. The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of infinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.

关键词： Asymptotic behaviour of eigenvalues boundary-value problems functional-conditions discontinuous coefficients

EIGENFUNCTIoN EXPANSIoN FoR STURM-LIoUVILLE PRoBLEMS WITH TRANSMISSIoN CoNDITIoNS AT oNE INTERIoR PoINT

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Acta Mathematica Scientia 2015年第3期35卷 639-649页

作者： oktay sh.mukhtarov Kadriye AYDEMIR Institute of Mathematics and Mechanics Azerbaijan National Academy of Sciences Department of Mathematics Faculty of ScienceGaziosmanpasa University

The purpose of this article is to extend some spectral properties of regular Sturm- Liouville problems to the special type discontinuous boundary-value problem, which consists of a Sturm-Liouville equation together with eigenparameter-dependent boundary conditions and two supplementary transmission conditions. We construct the resolvent operator and Green＇s function and prove theorems about expansions in terms of eigenfunctions in modified Hilbert space L2[a, b].

关键词： Boundary-value problems transmission conditions resolvent operator