Results 1 to 10 of about 567,385 (243)

Perturbations of periodic Sturm–Liouville operators [PDF]

Advances in Mathematics, 2021
We study perturbations of the self-adjoint periodic Sturm--Liouville operator \[ A_0 = \frac{1}{r_0}\left(-\frac{\mathrm d}{\mathrm dx} p_0 \frac{\mathrm d}{\mathrm dx} + q_0\right) \] and conclude under $L^1$-assumptions on the differences of the ...
J. Behrndt, Philipp Schmitz, G. Teschl, C. Trunk   +3 more
semanticscholar   +4 more sources

Traces and inverse nodal problem for Sturm–Liouville operators with frozen argument

Applied Mathematics Letters, 2020
In this paper, Sturm–Liouville operators with frozen argument are studied. We derive the regularized trace formulae for these operators. Also we provide asymptotic expressions for the nodal points and give a constructive procedure for solving an inverse ...
Yang Chuan-Fu, Yi Teng Hu, Natalia Bondarenko   +2 more
exaly   +2 more sources

Reconstruction for Sturm–Liouville operators with frozen argument for irrational cases

Applied Mathematics Letters, 2021
An inverse spectral problem for Sturm–Liouville operators with frozen argument irrationally proportioned to the interval length is studied in this paper. We present a constructive procedure for reconstructing the potential from the spectrum.
Yu Ping Wang, Wenju Zhao, Maozhu Zhang
exaly   +2 more sources

Sturm–Liouville operators on time scales [PDF]

Journal of Difference Equations and Applications, 2012
We establish the connection between Sturm-Liouville equations on time scales and Sturm--Liouville equations with measure-valued coefficients. Based on this connection we generalize several results for Sturm-Liouville equations on time scales which have been obtained by various authors in the past.
Jonathan Eckhardt, Gerald Teschl
exaly   +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

Random Sturm–Liouville operators

Applied Mathematics Letters, 2011
Selfadjoint Sturm-Liouville operators $H_ω$ on $L_2(a,b)$ with random potentials are considered and it is proven, using positivity conditions, that for almost every $ω$ the operator $H_ω$ does not share eigenvalues with a broad family of random operators and in particular with operators generated in the same way as $H_ω$ but in $L_2(\tilde a,\tilde b)$
Rafael René del Rio Castillo
exaly   +4 more sources

Spectral properties of an impulsive Sturm-Liouville operator. [PDF]

J Inequal Appl, 2018
This work is devoted to discuss some spectral properties and the scattering function of the impulsive operator generated by the Sturm-Liouville equation. We present a different method to investigate the spectral singularities and eigenvalues of the mentioned operator.
Bairamov E, Erdal I, Yardimci S.
europepmc   +6 more sources

Transformation operators for impedance Sturm–Liouville operators on the line

Математичні Студії, 2023
In the Hilbert space $H:=L_2(\mathbb{R})$, we consider the impedance Sturm--Liouville operator $T:H\to H$ generated by the differential expression $ -p\frac{d}{dx}{\frac1{p^2}}\frac{d}{dx}p$, where the function  $p:\mathbb{R}\to\mathbb{R}_+$ is of ...
M. Kazanivskiy, Ya. Mykytyuk, N. Sushchyk   +2 more
doaj   +2 more sources

Transformation Operators for Sturm-Liouville Operators with Singular Potentials [PDF]

Mathematical Physics Analysis and Geometry, 2004
Transformation operators are constructed for the Sturm-Liouville operator \(\ell f:=f''+qf\) with a singular complex-valued potential \(q\in W_2^{-1}(0,1)\). Some applications to the spectral analysis of Sturm-Liouville operators with singular potentials are also given.
Rostyslav Hryniv
exaly   +2 more sources

Spectral properties of singular Sturm–Liouville operators via boundary triples and perturbation theory [PDF]

Journal of Differential Equations, 2022
We apply both the theory of boundary triples and perturbation theory to the setting of semi-bounded Sturm-Liouville operators with two limit-circle endpoints.
Dale Frymark, C. Liaw
semanticscholar   +1 more source