Eigenparameter In Boundary Condition Research Articles

Asymptotic Estimations of Eigenvalues and Eigenfunctions for Nonlocal Boundary Value Problems with Eigenparameter-Dependent Boundary Conditions

The nonlocal boundary value problem with eigenparameter dependent boundary conditions is studied in this work. Firstly, we give the asymptotic expressions of the general solution for the equation corresponding to the initial conditions and prove the simplicity of eigenvalues. Moreover, the general properties of the eigenvalues and eigenfunctions for such a problem are proved. Finally, the asymptotic formulas of eigenvalues and eigenfunctions are obtained under certain mild conditions. Our method is to incorporate the perturbation theory and asymptotic analysis in the framework of classical Sturm-Liouville problems, which provides a different idea for the investigating of the Sturm-Liouville problems with eigenparameter in boundary conditions.

Scattering analysis of a quantum impulsive boundary value problem with spectral parameter

We are interested in scattering and spectral analysis of an impulsive boundary value problem (IBVP) generated with a $q$-difference equation with eigenparameter in boundary condition in addition to impulsive conditions. We work on the Jost solution and scattering function of this problem, and by using the scattering solutions, we establish the resolvent operator, continuous spectrum and point spectrum of this problem. Furthermore, we discuss asymptotic behavior of the Jost solution and properties of eigenvalues.Also, we illustrate our results by a detailed example which is the special case of main problem.

Spectral analysis of discrete dirac equation with generalized eigenparameter in boundary condition

Let L denote the discrete Dirac operator generated in ?2 (N,C2) by the non-selfadjoint difference operators of first order (an+1y(2)n+1 + bny(2)n + pny(1)n = ?y(1)n, an-1y(1)n-1 + bny(1)n + qny(2)n = ?y(2)n, n ? N, (0.1) with boundary condition Xp k=0 (y(2)1?k + y(1)0 ?k)?k=0, (0.2) where (an), (bn), (pn) and (qn), n ? N are complex sequences, ?i; ?i ? C, i = 0, 1, 2,..., p and ? is a eigenparameter. We discuss the spectral properties of L and we investigate the properties of the spectrum and the principal vectors corresponding to the spectral singularities of L, if ?? n=1 |n|(|1-an| + |1+bn| + |pn| + |qn|) < ? holds.

Sturm-Liouville Problems with finitely many point $\delta-$interactions and eigen-parameter in boundary condition

Sturm-Liouville Problems with finitely many point $\delta-$interactions and eigen-parameter in boundary condition

On impulsive Sturm–Liouville operators with singularity and spectral parameter in boundary conditions

We study properties and the asymptotic behavior of spectral characteristics for a class of singular Sturm–Liouville differential operators with discontinuity conditions and an eigenparameter in boundary conditions. We also determine theWeyl function for this problem and prove uniqueness theorems for a solution of the inverse problem corresponding to this function and spectral data.

A Dirac System with Transmission Condition and Eigenparameter in Boundary Condition

This paper deals with a Dirac system with transmission condition and eigenparameter in boundary condition. We give an operator-theoretic formulation of the problem then investigate the existence of the solution. Some spectral properties of the problem are studied.

On Computing of Eigenvalues of Differential Equations Q = λP with Eigenparameter in Boundary Conditions

Problem statement: Our purpose of this study is to use sinc methods to compute approximately the eigenval-ues of second-order operator pencil of the form Q-λP. Approach: Where Q is second order self adjoint differential operator and P is a first order and λ∈C is an eigenvalue parameter. Results: The eigenparameter appears in the boundary conditions linearly. Using computable error boundswe obtain eigenvalue enclosures in a simple way. Conclusion/Recommendations: We give some numerical examples and makecompanions with existing results.