scholarly journals Asymptotics of eigenvalues of regular Sturm-Liouville problems with eigenvalue parameter in the boundary condition for integrable potential

2010 ◽  
Vol 107 (2) ◽  
pp. 209 ◽  
Author(s):  
Haskiz Coskun ◽  
Elif Baskaya
Keyword(s):  
Boundary Condition ◽  
Asymptotic Estimates ◽  
Asymptotics Of Eigenvalues ◽  
Integrable Potential ◽  
Eigenvalue Parameter ◽  
Sturm Liouville

In this paper we obtain asymptotic estimates of eigenvalues for regular Sturm-Liouville problems having the eigenparameter in the boundary condition without smoothness conditions on $q$.

scholarly journals Asymptotic Approximations of Eigen-Functions for Regular Sturm-Liouville Problems with Eigenvalue Parameter in the Boundary Condition for Integrable Potential

2013 ◽  
Vol 113 (1) ◽  
pp. 143 ◽  
Author(s):  
Haskiz Coşkun ◽  
Ayşe Kabataş
Keyword(s):  
Boundary Condition ◽  
Asymptotic Approximations ◽  
Asymptotic Estimates ◽  
Integrable Potential ◽  
Eigenvalue Parameter ◽  
Sturm Liouville

In this paper we obtain asymptotic estimates of eigenfunctions for regular Sturm-Liouville problems having the eigenparameter in the boundary condition without smoothness conditions on the potential.

scholarly journals Essentially isospectral transformations and their applications

2017 ◽  
Author(s):  
Namig J. Guliyev
Keyword(s):  
Boundary Conditions ◽  
Existence Theorems ◽  
Dirichlet Boundary Conditions ◽  
Trace Formulas ◽  
Asymptotics Of Eigenvalues ◽  
Regularized Trace ◽  
Eigenvalue Parameter ◽  
Nevanlinna Functions ◽  
Sturm Liouville ◽  
Uniqueness And Existence

We define and study the properties of Darboux-type transformations between Sturm–Liouville problems with boundary conditions containing rational Herglotz–Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary conditions). Using these transformations, we obtain various direct and inverse spectral results for these problems in a unified manner, such as asymptotics of eigenvalues and norming constants, oscillation of eigenfunctions, regularized trace formulas, and inverse uniqueness and existence theorems.

scholarly journals Important Notes for a Fuzzy Boundary Value Problem

2019 ◽  
Vol 4 (2) ◽  
pp. 305-314 ◽  
Author(s):  
Hülya Gültekin Çitil
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Integral Equations ◽  
Boundary Value ◽  
Liouville Problem ◽  
Eigenvalue Parameter ◽  
Sturm Liouville ◽  
Fuzzy Boundary

AbstractIn this paper is studied a fuzzy Sturm-Liouville problem with the eigenvalue parameter in the boundary condition. Important notes are given for the problem. Integral equations are found of the problem.

scholarly journals Inverse problems for the Sturm–Liouville equation with a spectral parameter in the boundary condition

2017 ◽  
Author(s):  
Namig J. Guliyev
Keyword(s):  
Boundary Condition ◽  
Inverse Problems ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Equation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Eigenvalue Parameter ◽  
Sturm Liouville ◽  
Necessary And Sufficient

Inverse problems of recovering the coefficients of Sturm--Liouville problems with the eigenvalue parameter linearly contained in one of the boundary conditions are studied: (1) from the sequences of eigenvalues and norming constants; (2) from two spectra. Necessary and sufficient conditions for the solvability of these inverse problems are obtained.

Two-point boundary value problems with eigenvalue parameter contained in the boundary conditions

1977 ◽  
Vol 77 (3-4) ◽  
pp. 293-308 ◽  
Author(s):  
Charles T. Fulton
Keyword(s):  
Boundary Condition ◽  
Hilbert Space ◽  
Eigenfunction Expansion ◽  
Closed Interval ◽  
Heat Conduction Problem ◽  
Adjoint Operator ◽  
Point Boundary ◽  
Eigenvalue Parameter ◽  
Sturm Liouville ◽  
Regular Problems

SynopsisIn this paper it is shown that the analysis of Titchmarsh's book [32] for regular Sturm-Liouville problems on a finite closed interval carries over readily to regular problems involving the eigenvalue parameter in the boundary condition at one end-point. The manner in which this type of problem is associated with a self-adjoint operator in Hilbert space has recently been pointed out by Walter in [36], and his operator-theoretic formulation is adopted here. The use of the eigenfunction expansion is illustrated by applying it to solve a heat-conduction problem for a solid in contact with a fluid.

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