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Fractal Sturm–Liouville Theory

Fractal and Fractional
This paper provides a short summary of fractal calculus and its application to generalized Sturm–Liouville theory. It presents both the fractal homogeneous and non-homogeneous Sturm–Liouville problems and explores the theory’s applications in optics.
Alireza Khalili Golmankhaneh, Zoran Vidović, Hüseyin Tuna, Bilender P. Allahverdiev   +3 more
doaj   +4 more sources

Bernstein collocation technique for a class of Sturm-Liouville problems [PDF]

Heliyon
Sturm-Liouville problems have yielded the biggest achievement in the spectral theory of ordinary differential operators. Sturm-Liouville boundary value issues appear in many key applications in natural sciences. All the eigenvalues for the standard Sturm-
Humaira Farzana, Samir Kumar Bhowmik, M.A. Alim   +2 more
doaj   +2 more sources

Examining the Feasibility of the Sturm–Liouville Theory for Ross Recovery

Mathematics, 2020
Recent studies have suggested that it is feasible to recover a physical measure from a risk-neutral measure. Given a market state variable modeled as a Markov process, the key concept is to extract a unique positive eigenfunction of the generator of the ...
Shinmi Ahn, Hyungbin Park
doaj   +3 more sources

Relative oscillation theory for Sturm–Liouville operators extended

Journal of Functional Analysis, 2008
We extend relative oscillation theory to the case of Sturm--Liouville operators $H u = r^{-1}(-(pu')'+q u)$ with different $p$'s. We show that the weighted number of zeros of Wronskians of certain solutions equals the value of Krein's spectral shift function inside essential spectral gaps.
Gerald Teschl, Helge Kruger
exaly   +5 more sources

On the spectral theory of singular indefinite Sturm–Liouville operators

Journal of Mathematical Analysis and Applications, 2007
We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally has the same spectral properties as a definitizable operator.
Jussi Behrndt
exaly   +2 more sources

Spectral and Oscillation Theory for an Unconventional Fractional Sturm–Liouville Problem

Fractal and Fractional
Here, we investigate the spectral and oscillation theory for a class of fractional differential equations subject to specific boundary conditions.
Mohammad Dehghan, Angelo B. Mingarelli
doaj   +3 more sources

Relations between spectrum curves of discrete Sturm-Liouville problem with nonlocal boundary conditions and graph theory

Lietuvos Matematikos Rinkinys, 2021
Sturm-Liouville problem with nonlocal boundary conditions arises in many scientific fields such as chemistry, physics, or biology. There could be found some references to graph theory in a discrete Sturm-Liouville problem, especially in investigation of ...
Jonas Vitkauskas, Artūras Štikonas
doaj   +1 more source

Research on singular Sturm–Liouville spectral problems with a weighted function

Boundary Value Problems, 2022
As early as 1910, Weyl gave a classification of the singular Sturm–Liouville equation, and divided it into the Limit Point Case and the Limit Circle Case at infinity. This led to the study of singular Sturm–Liouville spectrum theory. With the development
Shuning Tang
doaj   +1 more source

On an Integral Equation with the Riemann Function Kernel

Axioms, 2022
This paper is concerned with a study of a special integral equation. This integral equation arises in many applied problems, including transmutation theory, inverse scattering problems, the solution of singular Sturm–Liouville and Shrödinger equations ...
Sergei Sitnik, Abdul Ahad Arian
doaj   +1 more source

A Study of the Eigenfunctions of the Singular Sturm–Liouville Problem Using the Analytical Method and the Decomposition Technique

Mathematics, 2020
The history of boundary value problems for differential equations starts with the well-known studies of D. Bernoulli, J. D’Alambert, C. Sturm, J. Liouville, L. Euler, G. Birkhoff and V. Steklov.
Oktay Sh. Mukhtarov, Merve Yücel
doaj   +1 more source