Solving inverse Sturm–Liouville problem with separated boundary conditions by using two different input data

2017 ◽  
Vol 95 (10) ◽  
pp. 1992-2010 ◽  
Author(s):  
Abdolali Neamaty ◽  
Shahrbanoo Akbarpoor ◽  
Emrah Yilmaz
Keyword(s):  
Boundary Conditions ◽  
Input Data ◽  
Liouville Problem ◽  
Separated Boundary Conditions ◽  
Sturm Liouville

scholarly journals A solution to the inverse problem for the Sturm-Liouville-type equation with a delay

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1237-1245 ◽  
Author(s):  
Milenko Pikula ◽  
Vladimir Vladicic ◽  
Olivera Markovic
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Fourier Coefficients ◽  
Liouville Problem ◽  
Type Equation ◽  
Liouville Type ◽  
Separated Boundary Conditions ◽  
Sturm Liouville ◽  
Delay Factor ◽  
Spectral Assignment

The paper is devoted to study of the inverse problem of the boundary spectral assignment of the Sturm-Liouville with a delay. -y'(x) + q(x)y(? ? x) = ?y(x), q ? AS[0, ?], ? ? (0,1] (1) with separated boundary conditions: y(0) = y(?) = 0 (2) y(0) = y'(?) = 0 (3) It is argued that if the sequence of eigenvalues is given ?n(1) and ?n(2) tasks (1-2) and (1-3) respectively, then the delay factor ? ? (0,1) and the potential q ? AS[0, ?] are unambiguous. The potential q is composed by means of trigonometric Fourier coefficients. The method can be easily transferred to the case of ? = 1 i.e. to the classical Sturm-Liouville problem.

scholarly journals A Prüfer approach to half-linear Sturm-Liouville problems

1998 ◽  
Vol 41 (3) ◽  
pp. 573-583 ◽  
Author(s):  
Patrick J. Browne
Keyword(s):  
Boundary Conditions ◽  
Liouville Problem ◽  
Oscillation Theory ◽  
Separated Boundary Conditions ◽  
Sturm Liouville ◽  
Image Position

We consider the half linear Sturm-Liouville problemon the interval [0,1] subject to separated boundary conditions (which may be eigenparameter dependent at x = 1) and use Prüfer techniques to produce an oscillation theory for this problem. Both right definite (r > 0) and left definite (r of both signs) cases are discussed.

Sturm—Liouville problems and discontinuous eigenvalues

1999 ◽  
Vol 129 (4) ◽  
pp. 707-716 ◽  
Author(s):  
W. N. Everitt ◽  
M. Möller ◽  
A. Zettl
Keyword(s):  
Boundary Conditions ◽  
Liouville Problem ◽  
Open Interval ◽  
Regular Boundary ◽  
End Points ◽  
The Real ◽  
Separated Boundary Conditions ◽  
Sturm Liouville ◽  
Discrete Spectra ◽  
Regular Problems

If a Sturm—Liouville problem is given in an open interval of the real line, then regular boundary value problems can be considered on compact sub-intervals. For these regular problems, all with necessarily discrete spectra, the eigenvalues depend on both the end-points of the compact intervals, and upon the choice of the real separated boundary conditions at these end-points. These eigenvalues are not, in general, continuous functionsof the end-points and boundary conditions. The paper shows the surprising form of these discontinuities. The results have applications to the approximations of singular Sturm—Liouville problems by regular problems, and to the theoretical aspects of the Sleign2 Computer program.

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.

Sign in / Sign up

Export Citation Format

Share Document