scholarly journals The Riesz Basis Property of an Indefinite Sturm–Liouville Problem with Non-Separated Boundary Conditions

2013 ◽  
Vol 77 (4) ◽  
pp. 533-557 ◽  
Author(s):  
Branko Ćurgus ◽  
Andreas Fleige ◽  
Aleksey Kostenko
Keyword(s):  
Boundary Conditions ◽  
Riesz Basis ◽  
Liouville Problem ◽  
Basis Property ◽  
Riesz Basis Property ◽  
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.

Riesz Basis Generation of the Euler-Bernoulli Beam Equation with Boundary Energy Dissipation

2012 ◽  
Vol 433-440 ◽  
pp. 123-127
Author(s):  
Cui Lian Zhou
Keyword(s):  
Energy Dissipation ◽  
Boundary Conditions ◽  
Riesz Basis ◽  
Boundary Energy ◽  
Basis Property ◽  
Beam Equation ◽  
Bernoulli Beam ◽  
Riesz Basis Property ◽  
Euler Bernoulli Beam ◽  
Regular Property

In this paper, the Riesz basis generation of the Euler-Bernoulli beam equation with with boundary energy dissipation is studied. Using the regular property of the boundary conditions, it is shown that the Riesz basis property holds

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.

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