On a boundary problem generated by a self-adjoint Sturm-Liouville differential operator on the entire real axis

1969 ◽  
Vol 6 (6) ◽  
pp. 873-879
Author(s):  
M. M. Gekhtman ◽  
I. V. Stankevich
Keyword(s):  
Differential Operator ◽  
Boundary Problem ◽  
Real Axis ◽  
Entire Real Axis ◽  
Sturm Liouville

25.—Spectrum of a Third-order Differential Operator with Large Coefficients

1975 ◽  
Vol 72 (4) ◽  
pp. 299-305
Author(s):  
K. Unsworth
Keyword(s):  
Differential Operator ◽  
Differential Expression ◽  
Real Axis ◽  
Sufficient Conditions ◽  
Order Differential Operator ◽  
Third Order ◽  
Minimal Operator ◽  
The Third ◽  
Entire Real Axis

SynopsisThis paper sets out to study the spectrum of self-adjoint extensions of the minimal operator associated with the third-order formally symmetric differential expression. The technique employed is the method of singular sequences. Sufficient conditions are established on the coefficients of the differential expression in order that the spectrum should cover the entire real axis. Particular cases in which the coefficients behave roughly as powers of x as the magnitude of x becomes large are then considered, and certain conclusions are drawn regarding the spectra under different restrictions on these powers of x.

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.

The Expansion Theorems for Sturm-Liouville Operators with an Involution Perturbation

2021 ◽  
Author(s):  
Abdizhahan Sarsenbi
Keyword(s):  
Differential Operator ◽  
Differential Operators ◽  
Second Order ◽  
Order Differential Operator ◽  
Spectral Expansions ◽  
Sturm Liouville ◽  
Complex Valued ◽  
Liouville Operators

In this work, we studied the Green’s functions of the second order differential operators with involution. Uniform equiconvergence of spectral expansions related to the second-order differential operators with involution is obtained. Basicity of eigenfunctions of the second-order differential operator operator with complex-valued coefficient is established.

scholarly journals Inverse spectral boundary problem Sturm Liouville type with constant delay and non-zero initial function

2021 ◽  
Vol 51 ◽  
pp. 18-30
Author(s):  
Milenko Pikula ◽  
Dragana Nedić ◽  
Ismet Kalco ◽  
Ljiljanka Kvesić
Keyword(s):  
Boundary Conditions ◽  
Spectral Problem ◽  
Boundary Problem ◽  
Initial Function ◽  
Inverse Spectral Problem ◽  
Constant Delay ◽  
Liouville Type ◽  
Sturm Liouville ◽  
Inverse Spectral ◽  
The Right

This paper is dedicated to solving of the direct and inverse spectral problem for Sturm Liouville type of operator with constant delay from 𝜋/2 to 𝜋, non-zero initial function and Robin’s boundary conditions. It has been proved that two series of eigenvalues unambiguously define the following parameters: delay, coefficients of delay within boundary conditions, the potential on the segment from the point of delay to the right-hand side of the distance and the product of the starting function and potential from the left end of the distance to the delay point.

scholarly journals Solutions of Linear Impulsive Differential Systems Bounded on the Entire Real Axis

2010 ◽  
Vol 2010 (1) ◽  
pp. 494379 ◽  
Author(s):  
Alexandr Boichuk ◽  
Martina Langerová ◽  
Jaroslava Škoríková
Keyword(s):  
Real Axis ◽  
Differential Systems ◽  
Entire Real Axis ◽  
Impulsive Differential Systems

scholarly journals A two-index generalization of conformable operators with potential applications in engineering and physics

2021 ◽  
Vol 67 (3 May-Jun) ◽  
pp. 429
Author(s):  
E. Reyes-Luis ◽  
G. Fernández Anaya ◽  
J. Chávez-Carlos ◽  
L. Diago-Cisneros ◽  
R. Muñoz Vega
Keyword(s):  
Differential Operator ◽  
Fractional Derivative ◽  
Fractional Order ◽  
Lagrange Equation ◽  
Conformable Fractional Derivative ◽  
Fractional Order Calculus ◽  
Integer Order ◽  
Standard Scenario ◽  
Potential Applications ◽  
Sturm Liouville

We developed a somewhat novel fractional-order calculus workbench as a certain generalization of the Khalil’s conformable derivative. Although every integer-order derivate can naturally be consistent with fully physical-sense problem’s quotation, this is not the standard scenario of the non-integer-order derivatives, even aiming physics systems’s modelling, solely.We revisited a particular case of the generalized conformable fractional derivative and derived a differential operator, whose properties overcome those of the integer-order derivatives, though preserving its clue advantages.Worthwhile noting, that two-fractional indexes differential operator we are dealing, departs from the single-fractional index framework, which typifies the generalized conformable fractional derivative. This distinction leads to proper mathematical tools, useful in generalizing widely accepted results, with potential applications to fundamental Physics within fractional order calculus. The later seems to be especially appropriate for exercising the Sturm-Liouville eigenvalue problem, as well as the Euler-Lagrange equation and to clarify several operator algebra matters.

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