Results 11 to 20 of about 465 (169)

Fractal Sturm–Liouville Theory [PDF]

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
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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
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Discontinuous Sturm‐Liouville Problems and Associated Sampling Theories [PDF]

Abstract and Applied Analysis, 2011
This paper investigates the sampling analysis associated with discontinuous Sturm‐Liouville problems with eigenvalue parameters in two boundary conditions and with transmission conditions at the point of discontinuity. We closely follow the analysis derived by Fulton (1977) to establish the needed relations for the derivations of the sampling theorems ...
M. M. Tharwat
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A metric Sturm–Liouville theory in two dimensions [PDF]

Calculus of Variations and Partial Differential Equations, 2019
A central result of Sturm-Liouville theory (also called the Sturm-Hurwitz Theorem) states that if $ϕ_k$ is a sequence of eigenfunctions of a second order differential operator on the interval $I \subset \mathbb{R}$, then any linear combination satisfies a uniform bound on the roots $$ \# \left\{x \in I:\sum_{k \geq n}{ a_k ϕ_k(x)} = 0 \right\} \geq n-1.
Stefan Steinerberger
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Some Further Insight into the Sturm–Liouville Theory

Mathematics
Some classical texts on the Sturm–Liouville equation (p(x)y′)′−q(x)y+λρ(x)y=0 are revised to highlight further properties of its solutions. Often, in the treatment of the ensuing integral equations, ρ=const is assumed (and, further, ρ=1).
Salvatore De Gregorio, Lamberto Lamberti, Paolo De Gregorio   +2 more
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Relative oscillation theory for Sturm–Liouville operators extended [PDF]

Journal of Functional Analysis, 2007
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.
Helge Krüger, Gerald Teschl
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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
openaire   +3 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
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Scattering theory of impulsive Sturm-Liouville equations

Filomat, 2017
In this paper, we investigate scattering theory of the impulsive Sturm-Liouville boundary value problem (ISBVP). In particular, we find the Jost solution and the scattering function of this problem. We also study the properties of the Jost function and the scattering function of this ISBVP.
Elgiz Bairamov, Yelda Aygar, Basak Eren
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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
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