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J-selfadjointness of a class of high-order differential operators with transmission conditions

Frontiers of Mathematics in China 2022年第6期17卷 1025-1035页

作者： Ji LI Meizhen XU School of Sciences Inner Mongolia University of TechnologyHohhot010051China

This paper is to investigate the J-selfadjointness of a class of high-order complex coefficients differential operators with transmission *** the Lagrange bilinear form of J-symmetric differential equations,the definition of J-selfadjoint differential operators and the method of matrix representation,we prove that the operator is J-selfadjoint operator,and the eigenvectors and eigen-subspaces corresponding to different eigenvalues are C-orthogonal.

关键词： High-order differential operator transmission conditions J-self-adjoint C-orthogonal

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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

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Green Function of Fourth-order Differential Operator with Eigenparameter-dependent Boundary and transmission conditions

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Acta Mathematicae Applicatae Sinica 2017年第2期33卷 311-326页

作者： Xin-yan ZHANG Jiong SUN School of Statistics and Mathematics Inner Mongolia University of Finance and Economics School of Mathematical Sciences Inner Mongolia University

We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green function of the operator is given.

关键词： fourth-order differential operator eigenparameter-dependent boundary conditions transmission conditions eigenvalues Green function

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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

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