Weak stability for an inverse Sturm–Liouville problem with finite spectral data and complex potential

2005 ◽  
Vol 21 (4) ◽  
pp. 1275-1290 ◽  
Author(s):  
Marco Marletta ◽  
Rudi Weikard
Keyword(s):  
Spectral Data ◽  
Complex Potential ◽  
Liouville Problem ◽  
Weak Stability ◽  
Sturm Liouville

scholarly journals Inverse Uniqueness in Interior Transmission Problem and Its Eigenvalue Tunneling in Simple Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Spectral Data ◽  
Liouville Problem ◽  
Transmission Problem ◽  
Index Of Refraction ◽  
One Dimensional ◽  
Far Fields ◽  
Sturm Liouville ◽  
Interior Transmission Problem

We study inverse uniqueness with a knowledge of spectral data of an interior transmission problem in a penetrable simple domain. We expand the solution in a series of one-dimensional problems in the far-fields. We define an ODE by restricting the PDE along a fixed scattered direction. Accordingly, we obtain a Sturm-Liouville problem for each scattered direction. There exists the correspondence between the ODE spectrum and the PDE spectrum. We deduce the inverse uniqueness on the index of refraction from the discussion on the uniqueness anglewise of the Strum-Liouville problem.

Eigenvalue bounds for the singular Sturm Liouville problem with a complex potential

2003 ◽  
Vol 36 (13) ◽  
pp. 3773-3787 ◽  
Author(s):  
B M Brown ◽  
M Langer ◽  
M Marletta ◽  
C Tretter ◽  
M Wagenhofer
Keyword(s):  
Complex Potential ◽  
Liouville Problem ◽  
Eigenvalue Bounds ◽  
Sturm Liouville

Sturm-Liouville Problem for Stationary Differential Operator with Nonlocal Two-Point Boundary Conditions

2006 ◽  
Vol 11 (1) ◽  
pp. 47-78 ◽  
Author(s):  
S. Pečiulytė ◽  
A. Štikonas
Keyword(s):  
Boundary Condition ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Liouville Problem ◽  
Complex Case ◽  
Qualitative Behavior ◽  
Point Boundary ◽  
Sturm Liouville

The Sturm-Liouville problem with various types of two-point boundary conditions is considered in this paper. In the first part of the paper, we investigate the Sturm-Liouville problem in three cases of nonlocal two-point boundary conditions. We prove general properties of the eigenfunctions and eigenvalues for such a problem in the complex case. In the second part, we investigate the case of real eigenvalues. It is analyzed how the spectrum of these problems depends on the boundary condition parameters. Qualitative behavior of all eigenvalues subject to the nonlocal boundary condition parameters is described.

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