Eigenvalues of a Class of Eigenparameter Dependent Third-Order Differential Operators

Bai, Yulin; Wang, Wanyi; Li, Kun; Zheng, Zhaowen

doi:10.1007/s44198-022-00032-1

Cited by 4 publications

(2 citation statements)

References 36 publications

(45 reference statements)

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“…[10,13,21,30]. Particularly, in recent papers, we generalized these results to third-order differential operators with eigen-dependent boundary conditions [5], and Ao et al considered the case of third-order differential operators with discontinuity [27].…”

Section: Introductionmentioning

confidence: 83%

Eigenvalues of Sturm-Liouville Problems With Eigenparameter Dependent Boundary and Interface Conditions

Zheng,

Li,

Zheng

2023

Mathematical Modelling and Analysis

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In this paper, a regular discontinuous Sturm-Liouville problem which contains eigenparameter in both boundary and interface conditions is investigated. Firstly, a new operator associated with the problem is constructed, and the self-adjointness of the operator in an appropriate Hilbert space is proved. Some properties of eigenvalues are discussed. Finally, the continuity of eigenvalues and eigenfunctions is investigated, and the differential expressions in the sense of ordinary or Fréchet of the eigenvalues concerning the data are given.

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Section: Introductionmentioning

confidence: 83%

Eigenvalues of Sturm-Liouville Problems With Eigenparameter Dependent Boundary and Interface Conditions

Zheng,

Li,

Zheng

2023

Mathematical Modelling and Analysis

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“…Later, he studied the dependence of eigenvalues on some parameters for the fifth-order differential operator [25]. Recently, the dependence of eigenvalue for third-order problems has been extended to eigenparameter-dependent case [26,27].…”

Section: Introductionmentioning

confidence: 99%

Dependence of eigenvalues for higher odd-order differential operator with transmission conditions

Ji,

2023

Preprint

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In this paper, we consider the dependence of eigenvalues on the parameter for higher odd-order differential operator with three types of boundary conditions and corresponding transmission conditions. By defining an appropriate Hilbert space and its inner product, we prove that the eigenvalues of the operators associated with the problem are real and discrete, and give the resolvent operators related to the differential operators. In addition, we show that the eigenvalues are not only continuously but also smoothly dependent on the parameters of the problem, and give the corresponding differential expressions. In particular, giving the Frechet derivatives of the eigenvalues concerning the coefficient functions q0, q1, · · · , qn and the derivatives of the eigenvalues with respect to the left and right sides of the inner discontinuity point c.

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Dependence of Eigenvalues of $$(2n + 1)$$ th Order Boundary Value Problems with Transmission Conditions

Lin¹

2023

J Nonlinear Math Phys

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This paper deals with some boundary value problems generated by $$(2n + 1)$$ ( 2 n + 1 ) th order differential equation with transmission conditions. After showing that these problems generate self-adjoint operators and the eigenvalues of the problems are real, we introduce the continuous dependence and differentiable dependence of eigenvalues on parameters: coefficient functions and weight function, boundary conditions, transmission conditions, as well as the endpoints and transmission points. In addition, we obtain the differential expressions of all given parameters respectively.

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Eigenvalues of a Class of Eigenparameter Dependent Third-Order Differential Operators

Cited by 4 publications

References 36 publications

Eigenvalues of Sturm-Liouville Problems With Eigenparameter Dependent Boundary and Interface Conditions

Eigenvalues of Sturm-Liouville Problems With Eigenparameter Dependent Boundary and Interface Conditions

Dependence of eigenvalues for higher odd-order differential operator with transmission conditions

Dependence of Eigenvalues of $$(2n + 1)$$ th Order Boundary Value Problems with Transmission Conditions

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