Expansion in eigenfunctions of a differential operator with nonregular boundary conditions

1982 ◽  
Vol 21 (4) ◽  
pp. 313-317
Author(s):  
J. Degutis
Keyword(s):  
Differential Operator ◽  
Boundary Conditions ◽  
Expansion In Eigenfunctions

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.

scholarly journals On the method demonstrating existence of eigenvalues for a differential operator with boundary conditions dependent on parameter

1971 ◽  
Vol 11 (3) ◽  
pp. 683-690
Author(s):  
Š. Strelicas ◽  
J. Degutis
Keyword(s):  
Differential Operator ◽  
Boundary Conditions

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Ш. И. Стрелиц, Ю. Э. Дегутис. Об одном методе доказательства существования собственных значений для одного дифференциального оператора с краевыми условиями, зависящими от параметра Š. Strelicas, J. Degutis. Apie vieną diferencialinio operatoriaus su kraštinėmis sąlygomis, priklausančiomis nuo parametro, nuosavų reikšmių egzistavimo įrodymo metodą

Semibounded Extensions of Singular Ordinary Differential Operators

1988 ◽  
Vol 31 (4) ◽  
pp. 432-438
Author(s):  
Allan M. Krall
Keyword(s):  
Differential Operator ◽  
Lower Bound ◽  
Boundary Conditions ◽  
Differential Operators ◽  
The Self ◽  
Limit Circle ◽  
Singular Differential Operator ◽  
Ordinary Differential Operators

AbstractThe self-adjoint extensions of the singular differential operator Ly = [(py’)’ + qy]/w, where p < 0, w > 0, q ≧ mw, are characterized under limit-circle conditions. It is shown that as long as the coefficients of certain boundary conditions define points which lie between two lines, the extension they help define has the same lower bound.

scholarly journals An observation problem for the Bessel differential operator

1984 ◽  
Vol 26 (1) ◽  
pp. 92-107 ◽  
Author(s):  
K.-D. Werner
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Differential Operator ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Parabolic Partial Differential Equation ◽  
Final State ◽  
Bessel Differential Operator ◽  
State Observability

AbstractIn this paper, the parabolic partial differential equation ut = urr + (1/r)ur − (v2/r2)u, where v ≥ 0 is a parameter, with Dirichlet, Neumann, and mixed boundary conditions is considered. The final state observability for such problems is investigated.

Differential operator with irregular splitting boundary conditions

1976 ◽  
Vol 19 (5) ◽  
pp. 451-456 ◽  
Author(s):  
A. P. Khromov
Keyword(s):  
Differential Operator ◽  
Boundary Conditions
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