In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functi...In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functions,we obtain not only the existence,the simplicity,and the interlacing properties of the real eigenvalues,but also the oscillation properties,orthogonality of the eigenfunctions,and the expansion theorem.Finally,we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.展开更多
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...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.展开更多
In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hil...In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.展开更多
The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representation...The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems,some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions.To best understand the result,an algorithm and some examples are posted.展开更多
In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem an...In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.展开更多
In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spect...In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spectrum of the operator D 2 ＋q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.展开更多
基金The authors are supported by National Natural Sciences Foundation of China(11961060,11671322)the Key Project of Natural Sciences Foundation of Gansu Province(18JR3RA084).
文摘In this article,we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions.By constructing some new Lagrange-type identities and two fundamental functions,we obtain not only the existence,the simplicity,and the interlacing properties of the real eigenvalues,but also the oscillation properties,orthogonality of the eigenfunctions,and the expansion theorem.Finally,we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.
基金Supported by the National Natural Science Foundation of China under Grant No.11561050supported by the Natural Science Foundation of Inner Mongolia under Grant No.2016BS0103,2014MS0701the Science and Technology Plan Projects of Inner Mongolia under Grant No.NJZY16141,NJZY16142,NJZY16143
文摘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.
基金supported by the National Natural Science Foundation of China(No.12461086)the Natural Science Foundation of Hubei Province(No.2022CFC016)。
文摘In this paper,we study a class of Sturm-Liouville problems,where the boundary conditions involve eigenparameters.Firstly,by defining a new inner product which depends on the transmission conditions,we obtain a new Hilbert space,on which the concerned operator A is self-adjoint.Then we construct the fundamental solutions to the problem,obtain the necessary and sufficient conditions for eigenvalues,and prove that the eigenvalues are simple.Finally,we investigate Green’s functions of such problem.
基金Supported by the National Natural Science Foundation of China (12261066, 11661059)the Natural Science Foundation of Inner Mongolia (2021MS01020)。
文摘The inverse spectral theory of a class of Atkinson-type Sturm-Liouville problems with non-self-adjoint boundary conditions containing the spectral parameter is investigated.Based on the so-called matrix representations of such problems and a special class of inverse matrix eigenvalue problems,some of the coefficient functions of the corresponding Sturm-Liouville problems are constructed by using priori known two sets of complex numbers satisfying certain conditions.To best understand the result,an algorithm and some examples are posted.
文摘In this paper, the inverse spectral problem of Sturm-Liouville operator with boundary conditions and jump conditions dependent on the spectral parameter is investigated. Firstly, the self-adjointness of the problem and the eigenvalue properties are given, then the asymptotic formulas of eigenvalues and eigenfunctions are presented. Finally, the uniqueness theorems of the corresponding inverse problems are given by Weyl function theory and inverse spectral data approach.
基金supported by Natural Science Foun- dation of Jiangsu Province of China (BK 2010489)the Outstanding Plan-Zijin Star Foundation of Nanjing University of Science and Technology (AB 41366)+1 种基金NUST Research Funding (AE88787)the National Natural Science Foundation of China (11071119)
文摘In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spectrum of the operator D 2 ＋q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.
