Reconstruction of the Sturm–Liouville Operator with Nonseparated Boundary Conditions and a Spectral Parameter in the Boundary Condition

2018 ◽  
Vol 69 (9) ◽  
pp. 1416-1423 ◽  
Author(s):  
Ch. G. Ibadzadeh ◽  
I. M. Nabiev
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Spectral Parameter ◽  
Liouville Operator ◽  
Nonseparated Boundary Conditions ◽  
Sturm Liouville

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.

scholarly journals A unuqueness theorem for Sturm-Lioville operators with eigenparameter dependent boundary conditions

2012 ◽  
Vol 43 (1) ◽  
pp. 145-152 ◽  
Author(s):  
Yu-Ping Wang
Keyword(s):  
Boundary Condition ◽  
Inverse Problem ◽  
Boundary Conditions ◽  
Uniqueness Theorem ◽  
Linear Function ◽  
Spectral Parameter ◽  
Finite Interval ◽  
Sturm Liouville ◽  
Fractional Linear Function ◽  
Liouville Operators

In this paper, we discuss the inverse problem for Sturm- Liouville operators with boundary conditions having fractional linear function of spectral parameter on the finite interval $[0, 1].$ Using Weyl m-function techniques, we establish a uniqueness theorem. i.e., If q(x) is prescribed on $[0,\frac{1}{2}+\alpha]$ for some $\alpha\in [0,1),$ then the potential $q(x)$ on the interval $[0, 1]$ and fractional linear function $\frac{a_2\lambda+b_2}{c_2\lambda+d_2}$  of the boundary condition are uniquely determined by a subset $S\subset \sigma (L)$ and fractional linear function $\frac{a_1\lambda+b_1}{c_1\lambda+d_1}$ of the boundary condition.

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