Separation of the Sturm–Liouville differential operator with an operator potential

2004 ◽  
Vol 156 (2) ◽  
pp. 387-394 ◽  
Author(s):  
A.S. Mohammed ◽  
H.A. Atia
Keyword(s):  
Differential Operator ◽  
Operator Potential ◽  
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.

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 Resolvent for Non-Self-Adjoint Differential Operator with Block-Triangular Operator Potential

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Aleksandr Mikhailovich Kholkin
Keyword(s):  
Differential Operator ◽  
Sufficient Conditions ◽  
Operator Potential ◽  
Triangular Operator

A resolvent for a non-self-adjoint differential operator with a block-triangular operator potential, increasing at infinity, is constructed. Sufficient conditions under which the spectrum is real and discrete are obtained.

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.

Sign in / Sign up

Export Citation Format

Share Document